Venn Diagrams and Probability

You need Java to see this.

Venn diagrams are a way of visualizing sets. This applet lets you = highlight=20 the set A, the set B, the universal set S, the empty set {}, the = complement of A=20 (Ac), the complement of B (Bc), the intersection of A and B (AB), the = union of A=20 and B (A or B), the intersection of the complement of A with B (AcB), = and the=20 intersection of A with the complement of B (ABc). One can think of the = relative=20 area of a set to the area of S as a probability. The picture uses that = analogy:=20 the numbers P(A) and P(B) are proportional to the area of A and the area = of B,=20 respectively; P(AB) is the area of the intersection of A and B, and P(A = or B) is=20 the area of the union of A and B.

You can drag the events=20 A and B around, which changes the probability of their intersection and = of their=20 union. When A and B do not overlap, they are said to be disjoint=20 or mutually exclusive. When the probability of the intersection of A = and B=20 equals the product of the probability of A and the probability of B = (when P(AB)=20 =3D P(A)=D7P(B)), A and B are independent.=20 Try to drag A or B to make P(AB) =3D P(A)=D7P(B); notice how hard it is = to make the=20 overlap just right: independence is a very special relationship between = events.=20 The scrollbars let you adjust the probability of A and the probability = of B.=20

=0A= ------=_NextPart_000_0000_01C283FA.710A0560 Content-Type: application/octet-stream Content-Transfer-Encoding: quoted-printable Content-Location: http://stat-www.berkeley.edu/users/stark/Java/irGrade.js // script irGrade: interactive, real-time grading; html formatting; = statistical functions,=0A= // linear algebra=0A= // copyright 1997, 1998, 1999, 2000, 2001, 2002. P.B. Stark, = stark@stat.berkeley.edu=0A= // Version 1.0=0A= // All rights reserved.=0A= =0A= // !!!!Beginning of the code!!!!=0A= =0A= var irGradeModTime =3D '2002/06/10/1110';=0A= // modification date and time=0A= var today =3D (new Date()).toLocaleString();=0A= var copyYr =3D '1997--2002. '; // copyright years=0A= var theChapters =3D = [-1,0,1,2,3.1,3.2,3.3,4.1,4.2,4.3,5.1,5.2,5.3,6,7,8.1,8.2,9,=0A= = 10,11,12,13,14.1,14.2,14.3,15,16.1,16.2,17.1,17.2,18,19.1,19.2,=0A= 20.1,20.2,20.3,21,22,23,24,25=0A= ]; // list of the chapters=0A= var cookieExpireDays =3D 10; // days for the cookies to endure=0A= var theChapter; // current chapter=0A= var type =3D 'LA'; // default question type is = 'literal answer'=0A= var newStyleAnswer =3D true; // flag for pop-up versus inline=0A= var ansText =3D ' '; // to display correct answer=0A= var pCtr =3D 1; // counter for problems=0A= var qCtr =3D 1; // counter for questions=0A= //var sCtr =3D 0; // counter for solved exercises=0A= var fCtr =3D 0; // counter for footnotes=0A= //var sEx =3D new Array(); // array for exercise numbers of = solved exercises=0A= //var sEnum =3D 0; // counter for displaying = solutions=0A= var footnotes =3D new Array(); // array of footnotes=0A= var key =3D new Array(); // key for self-graded exercises=0A= var boxList =3D new Array(); // list of images for self-graded = exercises=0A= var longKey =3D new Array(); // long answers for exercises=0A= var solutionCode =3D new Array(); // javascript code to evaluate = after writing solution=0A= var setNum; // current problem set number=0A= var isLab =3D false; // is this a problem set?=0A= var pbsURL =3D 'http://www.stat.berkeley.edu/~stark';=0A= // P.B. Stark's URL=0A= var pbsRef =3D 'P.B. = Stark';=0A= // link to author=0A= var fudgeFactor =3D 0.01; // relative tolerance for imprecise = numerical answers=0A= var absFudge =3D 1.e-20; // absolute tolerance for = identically zero answers=0A= var wrongHtm =3D '

Sorry, = wrong answer.

';=0A= // message for wrong answer=0A= var rightHtm =3D '

Correct!

';=0A= // message for right answer=0A= var dsmsHtm =3D '

';=0A= // to go on when answer is right=0A= var startHtm =3D ' ';=0A= var showAnsHtm =3D '

' +=0A= '

'; // to go on or show answer when answer = is wrong=0A= var inlinePrefix=3D"Q#:a#:";=0A= var bigPi =3D "3141592653";=0A= var rmin =3D 2.3e-308; // for numerical analysis=0A= var eps =3D 2.3e-16; // ditto=0A= var maxIterations =3D 100; // default iteration limit for = iterative algorithms=0A= var continueLab;=0A= var htmStuff;=0A= var randSeed; // seed of random number generator=0A= var CA =3D false;=0A= var sectionContext; // store chapter-specific initialization = script=0A= var qImgSrc =3D '../Graphics/answer_unknown.gif';=0A= var rightImgSrc =3D '../Graphics/answer_good.gif';=0A= var wrongImgSrc =3D '../Graphics/answer_bad.gif';=0A= var alphabet =3D = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p',=0A= 'q','r','s','t','u','v','w','x','y','z'=0A= ];=0A= var ALPHABET =3D = ['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P',=0A= 'Q','R','S','T','U','V','W','X','Y','Z'=0A= ];=0A= var Alphabet =3D ALPHABET;=0A= var cardinals =3D = ['zero','one','two','three','four','five','six','seven','eight','nine','t= en',=0A= = 'eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','= eighteen',=0A= = 'nineteen','twenty','twenty-one','twenty-two','twenty-three','twenty-four= ',=0A= = 'twenty-five','twenty-six','twenty-seven','twenty-eight','twenty-nine','t= hirty',=0A= = 'thirty-one','thirty-two','thirty-three','thirty-four','thirty-five','thi= rty-six',=0A= = 'thirty-seven','thirty-eight','thirty-nine','fourty','fourty-one','fourty= -two',=0A= = 'fourty-three','fourty-four','fourty-five','fourty-six','fourty-seven','f= ourty-eight',=0A= = 'fourty-nine','fifty','fifty-one','fifty-two','fifty-three','fifty-four',= 'fifty-five',=0A= = 'fifty-six','fifty-seven','fifty-eight','fifty-nine','sixty','sixty-one',= 'sixty-two',=0A= = 'sixty-three','sixty-four','sixty-five','sixty-six','sixty-seven','sixty-= eight',=0A= = 'sixty-nine','seventy','seventy-one','seventy-two','seventy-three','seven= ty-four',=0A= = 'seventy-five','seventy-six','seventy-seven','seventy-eight','seventy-nin= e',=0A= = 'eighty','eighty-one','eighty-two','eighty-three','eighty-four','eighty-f= ive',=0A= = 'eighty-six','eighty-seven','eighty-eight','eighty-nine','ninety',=0A= = 'ninety-one','ninety-two','ninety-three','ninety-four','ninety-five',=0A= = 'ninety-six','ninety-seven','ninety-eight','ninety-nine','one hundred'=0A= ];=0A= var Cardinals =3D = ['Zero','One','Two','Three','Four','Five','Six','Seven','Eight','Nine','T= en',=0A= = 'Eleven','Twelve','Thirteen','Fourteen','Fifteen','Sixteen','Seventeen','= Eighteen',=0A= = 'Nineteen','Twenty','Twenty-one','Twenty-two','Twenty-three','Twenty-four= ',=0A= = 'Twenty-five','Twenty-six','Twenty-seven','Twenty-eight','Twenty-nine','T= hirty',=0A= = 'Thirty-one','Thirty-two','Thirty-three','Thirty-four','Thirty-five','Thi= rty-six',=0A= = 'Thirty-seven','Thirty-eight','Thirty-nine','Fourty','Fourty-one','Fourty= -two',=0A= = 'Fourty-three','Fourty-four','Fourty-five','Fourty-six','Fourty-seven','F= ourty-eight',=0A= = 'Fourty-nine','Fifty','Fifty-one','Fifty-two','Fifty-three','Fifty-four',= 'Fifty-five',=0A= = 'Fifty-six','Fifty-seven','Fifty-eight','Fifty-nine','Sixty','Sixty-one',= 'Sixty-two',=0A= = 'Sixty-three','Sixty-four','Sixty-five','Sixty-six','Sixty-seven','Sixty-= eight',=0A= = 'Sixty-nine','Seventy','Seventy-one','Seventy-two','Seventy-three','Seven= ty-four',=0A= = 'Seventy-five','Seventy-six','Seventy-seven','Seventy-eight','Seventy-nin= e',=0A= = 'Eighty','Eighty-one','Eighty-two','Eighty-three','Eighty-four','Eighty-f= ive',=0A= = 'Eighty-six','Eighty-seven','Eighty-eight','Eighty-nine','Ninety',=0A= = 'Ninety-one','Ninety-two','Ninety-three','Ninety-four','Ninety-five',=0A= = 'Ninety-six','Ninety-seven','Ninety-eight','Ninety-nine','One hundred'=0A= ];=0A= var ordinals =3D = ['zeroth','first','second','third','fourth','fifth','sixth','seventh','ei= ghth',=0A= = 'ninth','tenth','eleventh','twelfth','thirteenth','fourteenth','fifteenth= ',=0A= = 'sixteenth','seventeenth','eighteenth','ninteenth','twentieth','twenty-fi= rst',=0A= = 'twenty-second','twenty-third','twenty-fourth','twenty-fifth','twenty-six= th',=0A= = 'twenty-seventh','twenty-eighth','twenty-ninth','thirtieth','thirty-first= ',=0A= = 'thirty-second','thirty-third','thirty-fourth','thirty-fifth','thirty-six= th',=0A= = 'thirty-seventh','thirty-eighth','thirty-ninth','fourtieth','fourty-first= ',=0A= = 'fourty-second','fourty-third','fourty-fourth','fourty-fifth','fourty-six= th',=0A= = 'fourty-seventh','fourty-eighth','fourty-ninth','fiftieth','fifty-first',=0A= = 'fifty-second','fifty-third','fifty-fourth','fifty-fifth','fifty-sixth',=0A= = 'fifty-seventh','fifty-eighth','fifty-ninth','sixtieth','sixty-first',=0A= = 'sixty-second','sixty-third','sixty-fourth','sixty-fifth','sixty-sixth',=0A= = 'sixty-seventh','sixty-eighth','sixty-ninth','seventieth','seventy-first'= ,=0A= = 'seventy-second','seventy-third','seventy-fourth','seventy-fifth','sevent= y-sixth',=0A= = 'seventy-seventh','seventy-eighth','seventy-ninth','eightieth','eighty-fi= rst',=0A= = 'eighty-second','eighty-third','eighty-fourth','eighty-fifth',=0A= = 'eighty-sixth','eighty-seventh','eighty-eightth','eighty-ninth','ninetiet= h',=0A= = 'ninety-first','ninety-second','ninety-third','ninety-fourth','ninety-fif= th',=0A= = 'ninety-sixth','ninety-seventh','ninety-eighth','ninety-ninth','hundredth= '=0A= ];=0A= var iteratives =3D ['no times','once','twice','thrice'];=0A= for (var i=3D4; i < cardinals.length; i++) {=0A= iteratives[i] =3D cardinals[i] + ' times';=0A= }=0A= var primes =3D [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, = 53];=0A= var nPrimes =3D [0, 0, 1, 2, 2, 3, 3, 4, 4, 4, // 0-9=0A= 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, // 10-19=0A= 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, // 20-29=0A= 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, // 30-39=0A= 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, // 40-49=0A= 15, 15, 15, 16]; // 50-53=0A= var allTheChars =3D = '~\`!1@2#3$4%5^6&7*8(9)0_-+=3DQqWwEeRrTtYyUuIiOoPp{[}]|\\AaSsDdFfGgHhJjKk= Ll:;' +=0A= '\"\'ZzXxCcVvBbNnMm<,>.?/';=0A= var faces =3D = ['Ace','two','three','four','five','six','seven','eight','nine','ten','Ja= ck',=0A= 'Queen','King'];=0A= var suits =3D ['spades','hearts','diamonds','clubs'];=0A= var colors =3D ['red','orange','yellow','green','blue','indigo','violet',=0A= = 'black','white','gray','silver','gold','brown','aqua','teal',=0A= 'fuschia','magenta','cyan','sage','turquoise','chartreuse',=0A= = 'mauve','periwinkle','umber','brick','marigold','seafoam','coral',=0A= 'purple','grape','cherry','beige','copper','sienna','baby = blue'=0A= ];=0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= // FUNCTION LIBRARY=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= =0A= // =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D STRING HANDLERS and = HTML GENERATORS =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= =0A= function trimBlanks(s){=0A= if (s =3D=3D null || s.length =3D=3D 0 ) { return(s); }=0A= while (s.charAt(s.length-1) =3D=3D ' ' ) { // trim trailing = blanks=0A= s =3D s.substring(0, s.length-1);=0A= }=0A= while (s.charAt(0) =3D=3D ' ') { // trim leading = blanks=0A= s =3D s.substring(1, s.length);=0A= }=0A= return(s);=0A= }=0A= =0A= function allBlanks(s) {=0A= if (s =3D=3D null || trimBlanks(s).length =3D=3D 0) {=0A= return(true);=0A= } else {=0A= return(false);=0A= }=0A= }=0A= =0A= function removeAllBlanks(s){=0A= if (s =3D=3D null || s.length =3D=3D 0 ) {=0A= return(s);=0A= }=0A= while (s.indexOf(' ') > -1 ) {=0A= s =3D s.substring(0, s.indexOf(' ')) + s.substring(s.indexOf(' = ')+1, s.length);=0A= }=0A= return(s);=0A= }=0A= =0A= function makeTopLevel(nameString,features) {=0A= // ensures the window is a top level window with name nameString=0A= if (window !=3D top) {=0A= window.open(window.location,nameString,features);=0A= window.close();=0A= parent.close();=0A= } else {=0A= window.name=3DnameString;=0A= }=0A= return(true);=0A= }=0A= =0A= function makeTopLevel(nameString){=0A= if (window !=3D top) {=0A= window.open(window.location,nameString,=0A= 'toolbar=3Dyes,location=3Dyes,status=3Dyes');=0A= window.close();=0A= parent.close();=0A= } else window.name=3DnameString;=0A= return(true);=0A= }=0A= =0A= function makeTopLevel(){=0A= if (window !=3D top) {=0A= window.open(window.location,'',=0A= 'toolbar=3Dyes,location=3Dyes,status=3Dyes');=0A= window.close();=0A= parent.close();=0A= }=0A= return(true);=0A= }=0A= =0A= function sticiRef() {=0A= // pops up a window with the pronunciation of SticiGui=0A= sticiWin =3D window.open('','sticiWin',=0A= = 'toolbar=3Dno,location=3Dno,directories=3Dno,status=3Dno,scrollbars=3Dyes= ,'+=0A= = 'resizable=3Dyes,width=3D200,height=3D30,top=3D5,left=3D5');=0A= sticiWin.document.write('How do you say = that?' +=0A= '

Pronounced

' +=0A= '

\"Sticky-Gooey\"

' +=0A= '');=0A= sticiWin.document.close();=0A= sticiWin.focus();=0A= return(true);=0A= }=0A= =0A= function glossRef(lnk) {=0A= // opens a glossary window, if not already open, and displays the = glossary entry=0A= // referred to in the link.=0A= window.open(lnk, target=3D"glossWin");=0A= return(true);=0A= }=0A= =0A= function trimToLowerCase(s) {=0A= // trim trailing blanks, convert to lower case=0A= if (s =3D=3D null || s.length =3D=3D 0 ) {=0A= return(s);=0A= }=0A= return(trimBlanks(s.toLowerCase()));=0A= }=0A= =0A= function allLetters(s){=0A= // return true if all characters in string s are letters (or trailing = blanks)=0A= var trimS =3D trimToLowerCase(s);=0A= var alpha=3D' -abcdefghijklmnopqrstuvwxyz';=0A= var truth =3D true;=0A= for (var i =3D 0; i < trimS.length; i++) {=0A= if(alpha.indexOf(trimS.charAt(i)) < 0) {=0A= truth =3D false;=0A= }=0A= }=0A= return(truth);=0A= }=0A= =0A= function removeCommas(s) { // removes commas from a putative number=0A= return(removeString(',',s));=0A= }=0A= =0A= function removeString(str,s) { // removes instances of the string str = from s.=0A= // kluge to avoid regular expressions=0A= var sOut =3D s;=0A= var s1;=0A= var strLen =3D str.length;=0A= var inx =3D s.indexOf(str);=0A= while (inx > -1) {=0A= s1 =3D s.substring(0,inx);=0A= if (inx < (s.length - strLen) ) {=0A= s1 +=3D s.substring(inx+strLen, s.length);=0A= }=0A= s =3D s1;=0A= inx =3D s.indexOf(str);=0A= }=0A= return(s);=0A= }=0A= =0A= function removeStrings(strArr,s) {=0A= for (var j=3D0; j < strArr.length; j++) {=0A= s =3D removeString(strArr[j], s);=0A= }=0A= return(s);=0A= }=0A= =0A= function parsePercent(s) {=0A= // parse a number that contains a % sign to turn it into a decimal = fraction=0A= var value;=0A= if (s.indexOf('%') =3D=3D -1) {=0A= value =3D parseFloat(trimBlanks(removeCommas(s)))=0A= } else {=0A= while (s.indexOf('%') !=3D -1) {=0A= s =3D s.substring(0,s.indexOf('%')) +=0A= s.substring(s.indexOf('%')+1,s.length)=0A= }=0A= value =3D parseFloat(trimBlanks(removeCommas(s)))/100;=0A= }=0A= return(value);=0A= }=0A= =0A= function evalNum(s) { // try to evaluate a string as a numeric value=0A= var value;=0A= var dmy =3D s + ' ';=0A= dmy =3D dmy.replace(/\%/g,'\/100');=0A= dmy =3D dmy.replace(/,/g,'');=0A= if ( typeof(s) =3D=3D 'undefined' || s =3D=3D null || !s.match(/[^ = ]/) ) {=0A= value =3D 'NaN';=0A= } else if ( dmy.match(/[^1234567890+*\/.ed() -]/i) ) {=0A= value =3D 'NaN';=0A= } else if ( !dmy.match(/[1234567890]/) ) {=0A= value =3D 'NaN';=0A= } else {=0A= eval('value =3D ' + dmy + ';');=0A= }=0A= return(value);=0A= }=0A= =0A= function parseMultiple(option) {=0A= // pre-processes multiple selections so that checkAnswer can be used = to grade them=0A= var response =3D '';=0A= for (var i=3D0; i < option.length; i++) {=0A= if (option[i].selected) {=0A= response +=3D trimToLowerCase(option[i].value) + ',' ;=0A= }=0A= }=0A= if (response.charAt(response.length - 1) =3D=3D ',') { // trim = trailing comma=0A= response =3D response.substring(0, response.length - 1);=0A= }=0A= return(response);=0A= }=0A= =0A= function getFormElementIndex(q) {=0A= // finds the form element named q and returns its index.=0A= for (var inx =3D0; inx < document.forms[0].elements.length; inx++) {=0A= if (document.forms[0].elements[inx].name =3D=3D q)=0A= return(inx);=0A= }=0A= alert('Error #1 in irGrade.getFormElementIndex(): Form element ' + q = + ' is missing!');=0A= return('document.forms[0].length');=0A= }=0A= =0A= function findNum(s) {=0A= // if s is an integer or its string representation, returns s.=0A= // if not, tries to remove characters to=0A= // leave an int, and returns that int.=0A= var i =3D parseInt(s);=0A= if ( !isNaN(i)) {=0A= return(i);=0A= } else {=0A= var q =3D '';=0A= for (var j=3D0; j < s.length; j++) {=0A= var dum =3D q;=0A= if (!isNaN(parseInt(dum + s.charAt(j)))) {=0A= q +=3D s.charAt(j);=0A= }=0A= }=0A= return(q);=0A= }=0A= }=0A= =0A= function vFindNum(s) { // finds numbers in a string array=0A= var a =3D new Array(s.length);=0A= for (var i=3D0; i < s.length; i++) { a[i] =3D findNum(s[i]);}=0A= return(a);=0A= }=0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= COOKIE MANIPULATION = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=0A= =0A= function expireTimeString(ed) {=0A= var now =3D new Date();=0A= var expire =3D new Date();=0A= var cookDays;=0A= if (typeof(ed) =3D=3D 'undefined' || ed =3D=3D null) {=0A= cookDays =3D cookieExpireDays;=0A= } else {=0A= cookDays =3D ed;=0A= }=0A= expire.setTime(now.getTime() + cookDays*60*60*1000*24);=0A= return(expire.toGMTString());=0A= }=0A= =0A= function getCookieVal(cook,key){ // gets the value of key within the = cookie cook=0A= var searchStr =3D cook + '&';=0A= var val =3D null;=0A= var pat =3D key + '=3D';=0A= var inx =3D searchStr.indexOf(pat);=0A= if (inx > -1){=0A= searchStr =3D searchStr.substring(inx + pat.length, = searchStr.length);=0A= val =3D unescape(searchStr.substring(0, searchStr.indexOf('&')));=0A= }=0A= return(val);=0A= }=0A= =0A= function getCookieArray(cook,stem,len) { // gets an array from the cookie=0A= var ansArr =3D new Array(len);=0A= for (var i=3D0; i < len; i++) {=0A= ansArr[i] =3D getCookieVal(cook, stem + i.toString());=0A= }=0A= return(ansArr);=0A= }=0A= =0A= function setCookieArray(arr,stem) { // make a cookie-like string from = the array arr=0A= var ansStr =3D '';=0A= for (var i=3D0; i < arr.length; i++) {=0A= ansStr +=3D stem + i.toString() + '=3D' + arr[i] + '&';=0A= }=0A= if (ansStr.substr(ansStr.length-1,1) =3D=3D '&') {=0A= ansStr =3D ansStr.substring(0, ansStr.length - 1);=0A= }=0A= return(ansStr);=0A= }=0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= PROBLEM AND GRADING SUBROUTINES = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= =0A= function numToMultiple(opt,ans) { // finds the multiple choice closest = to ans=0A= var dif =3D Math.abs(parsePercent(opt[0]) - ans);=0A= var aVal =3D 'a';=0A= for (var i=3D1; i < opt.length; i++) {=0A= var d2 =3D Math.abs(parsePercent(opt[i]) - ans);=0A= if (d2 < dif) {=0A= dif =3D d2;=0A= aVal =3D alphabet[i];=0A= }=0A= }=0A= return(aVal);=0A= }=0A= =0A= function hiddenInput(string, val){ // hidden input with name=3D"string" = and value=3D"val"=0A= var s =3D "";=0A= return(s);=0A= }=0A= =0A= function textExercise(size,q,ca,checkFun) {=0A= // text input area of "size" size, name q, and appropriate onChange()=0A= var s =3D "";=0A= return(s);=0A= }=0A= =0A= function textProblem(size,q) { // makes text input area of "size" size, = name "q"=0A= var s =3D "";=0A= return(s);=0A= }=0A= =0A= function startExercise(q) { // writes html to start an exercise, = numbered q=0A= var s;=0A= if (HI) {=0A= s =3D "Problem " + q.toString() + ".";=0A= } else {=0A= s =3D "Exercise " + q.toString() + ".";=0A= }=0A= return(s);=0A= }=0A= =0A= function startProblem(q) { // writes html to start a problem, numbered q=0A= var s;=0A= if (HI) {=0A= s =3D "Problem " + q.toString() + ".";=0A= } else {=0A= s =3D "Exercise " + q.toString() + ".";=0A= }=0A= return(s);=0A= }=0A= =0A= function startSolution(q) { // html to start a solution, numbered q=0A= var s;=0A= if (HI) {=0A= s =3D "Solution to Problem " + q.toString() + = ".";=0A= } else {=0A= s =3D "Solution to Exercise " + q.toString() + = ".";=0A= }=0A= return(s);=0A= }=0A= =0A= function writeSelectExercise(mult, q, opt, ans) {=0A= document.writeln(selectExerciseString(mult, q, opt, ans));=0A= return(true);=0A= }=0A= =0A= function selectExerciseString(mult, q, opt, ans) {=0A= var name =3D 'Q' + q.toString();=0A= var s =3D selectExercise(mult, name, opt, CA);=0A= if (CA) {=0A= if (mult) {=0A= s +=3D '';=0A= }=0A= if (newStyleAnswer !=3D null && newStyleAnswer) {=0A= boxList[q - 1] =3D document.images.length;=0A= s +=3D '' +=0A= '

';=0A= }=0A= }=0A= key[q - 1] =3D ans;=0A= return(s);=0A= }=0A= =0A= function writeTextExercise(size, q, ans) { // does all the printing for = a textfield exercise=0A= document.writeln(textExercise(size, 'Q' + q, CA));=0A= var cf =3D false;=0A= if (typeof(ans) =3D=3D 'function') { // TO DO: allow functional = checks of answers.=0A= cf =3D true;=0A= }=0A= if (CA) {=0A= if (newStyleAnswer !=3D null && newStyleAnswer) {=0A= boxList[q - 1] =3D document.images.length;=0A= document.writeln('' +=0A= ' 3D"click

');=0A= }=0A= }=0A= key[q - 1] =3D ans;=0A= return(true);=0A= }=0A= =0A= function writeRadioExercise(q, opt, ans) { // write a radio exercise=0A= document.writeln(radioExercise('Q'+q, opt, CA));=0A= if (CA) {=0A= if (newStyleAnswer !=3D null && newStyleAnswer) {=0A= boxList[q - 1] =3D document.images.length;=0A= document.writeln('' +=0A= '

');=0A= }=0A= }=0A= key[q-1] =3D ans;=0A= return(true);=0A= }=0A= =0A= function radioExercise(q, opt, ca){ // makes a collection of radio = inputs.=0A= var s =3D "";=0A= var oplen =3D opt.length;=0A= for (var i =3D 0; i < oplen; i++) {=0A= s +=3D '\n' + alphabet[i] + ') ' + opt[i] + '
\n';=0A= }=0A= return(s);=0A= }=0A= =0A= function selectExercise(mult, q, opt, ca) {=0A= // makes a select with multiple=3Dmult, name q.=0A= // if mult, makes the size large enough to show all options.=0A= // otherwise size=3D1; opt is a 1 by array.=0A= var s;=0A= var size;=0A= var oplen =3D opt.length;=0A= if (mult) { // leave room for all the answers to be visible.=0A= size=3D oplen+1;=0A= } else {=0A= size =3D 1;=0A= }=0A= var s =3D '';=0A= return(s);=0A= }=0A= =0A= function scoreProblem(truth,response){=0A= var answer =3D parseKey(truth);=0A= response =3D trimToLowerCase(response);=0A= var rsp;=0A= var correctness;=0A= if (response =3D=3D null) {=0A= correctness =3D false;=0A= } else if (type =3D=3D 'WC') {=0A= rsp =3D trimBlanks(response);=0A= if (rsp.length > 0) {correctness =3D true};=0A= } else if (type =3D=3D 'LA') {=0A= // try to parse as number; if fail, take literal.=0A= rsp =3D evalNum(response);=0A= if (!isNaN(rsp)) {=0A= response =3D rsp;=0A= // if (response.indexOf('%') !=3D -1) {=0A= // rsp =3D parsePercent(response);=0A= // if (!isNaN(rsp)) {=0A= // response =3D rsp;=0A= // }=0A= // } else if = (!isNaN(parseFloat(trimBlanks(removeCommas(response))))) {=0A= // response =3D = parseFloat(trimBlanks(removeCommas(response)));=0A= }=0A= if (answer.toString() =3D=3D response.toString()) {=0A= correctness =3D true;=0A= } else {=0A= correctness =3D false;=0A= }=0A= } else if (type =3D=3D 'RG') {=0A= var r =3D evalNum(response);=0A= if ((answer[0] <=3D r) && (r <=3D answer[1])) {=0A= correctness =3D true;=0A= } else {correctness =3D false;}=0A= } else if (type =3D=3D 'MA') {=0A= correctness =3D false;=0A= for (var i=3D0; i < answer.length; i++) {=0A= if (response =3D=3D answer[i]) {=0A= correctness =3D true;=0A= }=0A= }=0A= } else if (type =3D=3D 'MR') {=0A= correctness =3D false;=0A= resArray =3D response.split(',');=0A= resArray.sort()=0A= if (resArray.length =3D=3D answer.length) {=0A= correctness =3D true;=0A= for (var i=3D0; i < answer.length; i++ ) {=0A= if (answer[i] !=3D trimToLowerCase(resArray[i])) {=0A= correctness =3D false;=0A= }=0A= }=0A= }=0A= }=0A= return(correctness);=0A= }=0A= =0A= function parseKey(s) {=0A= // parses the answer keys for interactive grading. See header.=0A= s =3D trimBlanks(s.toLowerCase()) // use only lower-case letters=0A= var answer;=0A= if (s.indexOf(':') !=3D -1) { // solution is a range=0A= answer =3D s.split(':')=0A= if (answer.length !=3D 2) { alert('Error #1 in = irGrade.parseKey(): bad range syntax!') }=0A= type =3D 'RG' // answer is of type range (RG)=0A= for (var i=3D0; i < answer.length; i++) {=0A= answer[i] =3D parsePercent(answer[i]);=0A= if (isNaN(answer[i])){=0A= alert('Error #2 in irGrade.parseKey(): unparsable number = in range!');=0A= }=0A= }=0A= ansText =3D answer[0] + ' to ' + answer[1];=0A= } else if (s.indexOf('&') !=3D -1 ){ // multiple required answers; = assume all=0A= // are letters=0A= answer =3D s.split('&');=0A= type =3D 'MR' // answer is of type multiple = required (MR)=0A= for (var i=3D0; i < answer.length; i++ ) {=0A= answer[i] =3D trimBlanks(answer[i].toLowerCase());=0A= answer.sort();=0A= }=0A= ansText =3D answer[0];=0A= for (var i=3D1; i < answer.length; i++) {=0A= ansText +=3D ' and ' + answer[i];=0A= }=0A= } else if (s.indexOf('|') !=3D -1 ){ // multiple answers accepted; = assume all=0A= // are letters=0A= answer =3D s.split('|');=0A= type =3D 'MA'; // answer is of type multiple = accepted (MA)=0A= for (var i=3D0; i < answer.length; i++ ) {=0A= answer[i] =3D trimBlanks(answer[i].toLowerCase());=0A= }=0A= ansText =3D answer[0];=0A= for (var i=3D1; i < answer.length; i++) {=0A= ansText +=3D ' or ' + answer[i];=0A= }=0A= } else if (s =3D=3D '*') {=0A= type =3D 'WC'; // wildcard=0A= answer =3D '*';=0A= ansText =3D 'any non-blank answer';=0A= } else { // answer is literal=0A= type =3D 'LA' // literal answer (LA)=0A= answer =3D parsePercent(s);=0A= if (isNaN(answer)) {=0A= answer =3D trimBlanks(s.toLowerCase());=0A= }=0A= ansText =3D answer;=0A= }=0A= return(answer);=0A= }=0A= =0A= function setCourse(inx) {=0A= setCourseSpecs(inx);=0A= document.applets[0].getSidFile(courses[inx][1] + sFileBase);=0A= return(document.applets[0].setBox(courses[inx][1] + dFileBase));=0A= }=0A= =0A= function setCourseSpecs(inx) {=0A= course =3D courses[inx][1];=0A= courseName =3D courses[inx][2];=0A= teacher =3D courses[inx][3];=0A= teacherName =3D courses[inx][4];=0A= gPath =3D courses[inx][5];=0A= dFile =3D cRoot + course + dFileBase;=0A= var sFile =3D cRoot + course + sFileBase;=0A= }=0A= =0A= function setDFile(inx) {=0A= setCourseSpecs(inx);=0A= document.forms[0].elements["dFile"].value =3D dFile;=0A= document.forms[0].elements["class"].value =3D courses[inx][1];=0A= return(true);=0A= }=0A= =0A= function writeCourseOptions(fun) {=0A= document.writeln('Course:');=0A= return(true);=0A= }=0A= =0A= function spawnGradePage(theForm) {=0A= if (validateLablet(theForm)) {=0A= var scorQStr =3D scoreBase + "class=3D" + course + "&gpath=3D" + = gPath +=0A= "&teacher=3D" + teacher;=0A= var queryURL =3D queryBase + "class=3D" + course + "&gpath=3D" + = gPath +=0A= "&teacher=3D" + teacher + "&sid=3D" + = theForm.sid.value +=0A= "&passwd=3D" + escape(theForm.sid.value) + = "&dFile=3D" + dFile +=0A= "&querylist=3D" + queryList;=0A= var histURL =3D '../Grades/scoreHist.htm';=0A= gradePage =3D = open('',"gradePage",'toolbar=3Dyes,location=3Dno,directories=3Dno,status=3D= yes,'+=0A= 'scrollbars=3Dyes,resizable=3Dyes');=0A= gradePage.document.open();=0A= gradePage.scorQStr =3D scorQStr;=0A= gradePage.teacherName =3D teacherName;=0A= gradePage.courseName =3D courseName;=0A= gradePage.semester =3D semester;=0A= gradePage.document.writeln("SticiGui Grade = Query");=0A= gradePage.document.writeln("");=0A= gradePage.document.writeln("");=0A= gradePage.document.writeln("");=0A= gradePage.document.writeln("");=0A= gradePage.document.close();=0A= return(true);=0A= } else {=0A= return(false);=0A= }=0A= }=0A= =0A= function spawnProblem(theForm,i) {=0A= if (validateLablet(theForm)) {=0A= var ck =3D document.cookie;=0A= var fname =3D formStemName + i.toString();=0A= var assigned =3D document.applets[0].isAssigned(fname);=0A= if (!assigned) {=0A= alert('This problem set is not yet assigned.\n' +=0A= 'Try again later.');=0A= return(false);=0A= }=0A= var sstr =3D crypt("sid" + theForm.sid.value, = theForm.sid.value) + '=3D';=0A= if (ck.indexOf(sstr) < 0){=0A= var rs =3D (theForm.sid.value).toString();=0A= if (rs.length < 10){ =0A= rs +=3D rs;=0A= }=0A= randSeed =3D parseInt(rs.substr(0,Math.min(10,rs.length)));=0A= setSubmitCookie("sid", theForm, true);=0A= ck =3D document.cookie;=0A= if (ck.indexOf(sstr) < 0){=0A= alert('Error #1 in irGrade.spawnProblem()!\n' +=0A= 'Make sure your browser is configured to accept = cookies.\n' +=0A= 'Clear existing cookies and try again.');=0A= return(false);=0A= }=0A= }=0A= var ss =3D ck.substring(ck.indexOf(sstr) + sstr.length, = ck.length);=0A= if (ss.indexOf(';') > -1) {ss =3D = ss.substring(0,ss.indexOf(';'))};=0A= var cl =3D crypt(ss, theForm.sid.value);=0A= var instr =3D '../Problems/set' + i.toString() + 'i.htm';=0A= var appl =3D '../Problems/set' + i.toString() + 'j.htm';=0A= lablet =3D = open('',"lablet",'toolbar=3Dno,location=3Dno,directories=3Dno,status=3Dno= ,'+=0A= 'scrollbars=3Dyes,resizable=3Dyes');=0A= lablet.document.open();=0A= lablet.continueLab =3D cl;=0A= var reveal =3D document.applets[0].revealKey(fname);=0A= var allowSubmit =3D document.applets[0].allowSubmit(fname);=0A= lablet.reveal =3D reveal;=0A= lablet.allowSubmit =3D allowSubmit;=0A= lablet.dFile =3D dFile;=0A= lablet.course =3D course;=0A= lablet.teacher =3D teacher;=0A= lablet.document.writeln("SticiGui Problem Set = " + i=0A= +"");=0A= lablet.document.writeln("");=0A= lablet.document.writeln("");=0A= lablet.document.writeln("");=0A= lablet.document.writeln("");=0A= lablet.document.close();=0A= return(true);=0A= } else {=0A= return(false);=0A= }=0A= }=0A= =0A= function checkAnswer(number, response) {=0A= // check response against key[number-1]. If number is not an integer,=0A= // calls findNum(number) to remove characters to try to leave an = integer.=0A= var theQuestion =3D findNum(number);=0A= var truth =3D scoreProblem(key[theQuestion-1],response);=0A= if (truth) {=0A= document.images[boxList[theQuestion-1]].src =3D rightImgSrc;=0A= } else {=0A= document.images[boxList[theQuestion-1]].src =3D wrongImgSrc;=0A= }=0A= return(truth);=0A= }=0A= =0A= function isAnswered(qVal) { // checks whether the student answered a = question=0A= var n =3D findNum(qVal) - 1;=0A= var iA =3D false;=0A= var inx;=0A= var el =3D document.forms[0].elements[qVal];=0A= var qT =3D el.type;=0A= if (qT =3D=3D 'select-one') {=0A= inx =3D el.selectedIndex;=0A= if (inx > 0) {=0A= iA =3D true;=0A= }=0A= } else if (qT =3D=3D 'select-multiple') {=0A= resp =3D parseMultiple(el.options);=0A= if (resp !=3D null && resp !=3D '' && resp !=3D '?') {=0A= iA =3D true;=0A= }=0A= } else if (qT =3D=3D 'text') {=0A= resp =3D el.value;=0A= if (resp !=3D null && resp !=3D '' && removeAllBlanks(resp) !=3D = null &&=0A= removeAllBlanks(resp).length > 0) {=0A= iA =3D true;=0A= }=0A= } else if (qT =3D=3D 'radio') { // incomprehensible bugs with this=0A= for (var i=3D0; i < el.length; i++) {=0A= if (el[i].checked) {=0A= iA =3D true;=0A= }=0A= }=0A= } else if ( typeof(qT) =3D=3D 'undefined' || qT =3D=3D null ) { // = assume it is a radio=0A= for (var i=3D0; i < el.length; i++) {=0A= if (el[i].checked) {=0A= iA =3D true;=0A= }=0A= }=0A= } else {=0A= alert('Error #1 in irGrade.js.isAnswered(): input type ' + qT +=0A= ' is not supported!');=0A= }=0A= return(iA);=0A= }=0A= =0A= =0A= function giveAnswer(number) {=0A= // display the answer to question[number] in a new window, provided the = student has=0A= // tried to answer the question=0A= answer =3D parseKey(key[findNum(number)-1]);=0A= ansWin =3D window.open('','ansWin',=0A= 'toolbar=3Dno,location=3Dno,directories=3Dno,status=3Dno,' +=0A= 'scrollbars=3Dyes,resizable=3Dyes,width=3D230,height=3D160');=0A= ansWin.document.write(startHtm);=0A= if (isAnswered(number)) {=0A= ansWin.document.write('

The correct answer = is
\n' +=0A= '' + ansText + '.

\n' + = dsmsHtm + endHtm);=0A= } else {=0A= ansWin.document.write('

You must answer = before you can ' +=0A= 'see the solution.' + dsmsHtm + endHtm);=0A= }=0A= return(true);=0A= }=0A= =0A= function validEmail(e) { // checks whether e appears to be a valid email = address=0A= var okEmailChars=3D"._-@:%0123456789abcdefghijklmnopqrstuvwxyz";=0A= var truth =3D true;=0A= if (e =3D=3D null || e.length =3D=3D 0) {=0A= truth=3Dfalse;=0A= } else {=0A= et =3D trimToLowerCase(e);=0A= if (et.indexOf('@') =3D=3D -1 ||=0A= ( (et.lastIndexOf('.') !=3D et.length - 4 ) &&=0A= (et.lastIndexOf('.') !=3D et.length - 3 ) ) )=0A= truth =3D false;=0A= else if (et.indexOf('@') !=3D et.lastIndexOf('@')) {=0A= truth =3D false;=0A= } else {=0A= for (var i=3D0; i < et.length; i++) {=0A= if(okEmailChars.indexOf(et.charAt(i)) < 0) {truth =3D = false;}=0A= }=0A= }=0A= }=0A= return(truth);=0A= }=0A= =0A= function validSID(s){ // check whether SID is valid=0A= var digits=3D"0123456789";=0A= var truth =3D false;=0A= if (s.length =3D=3D 8 && s.charAt(0) =3D=3D "1" || s.length =3D=3D = 9) {=0A= truth =3D true;=0A= for (var i=3D0; i < s.length; i++){=0A= if (digits.indexOf(s.charAt(i)) < 0) {truth =3D false;}=0A= }=0A= }=0A= return(truth);=0A= }=0A= =0A= function validateLabletSubmit(theForm){=0A= // check that various form entries are filled in correctly, submit or = cancel=0A= if (validateLablet(theForm)){=0A= return(labletSubmit(theForm));=0A= } else {=0A= return(false);=0A= }=0A= }=0A= =0A= function labletSubmit(theForm) {=0A= theForm.submitTime =3D new Date();=0A= confirmStr =3D 'Your assignment is ready to submit, ' +=0A= theForm.firstName.value + ' ' +=0A= theForm.lastName.value +=0A= '.\nPress \"OK\" to submit it now, or \"Cancel\" to return to = the assignment.';=0A= if (confirm(confirmStr)){=0A= setExtraInputs(theForm);=0A= setSubmitCookie(setNum.toString(),theForm,false);=0A= document.forms[1].action =3D = "http://www.stat.berkeley.edu/cgi-bin/grader";=0A= var s =3D collectResponses(theForm,true,true);=0A= document.forms[1].elements['contents'].value =3D crypt(s,bigPi);=0A= document.forms[1].submit();=0A= return(true);=0A= } else {=0A= alert("Your assignment has NOT been submitted.");=0A= return(false);=0A= }=0A= }=0A= =0A= function validateLablet(theForm) {=0A= if (theForm.lastName.value =3D=3D null || = theForm.lastName.value.length =3D=3D 0 ||=0A= allBlanks(theForm.lastName.value) ) {=0A= alert('Last Name is missing');=0A= theForm.lastName.focus();=0A= return(false);=0A= } else if (!allLetters(theForm.lastName.value) ) {=0A= alert('Illegal character(s) in Last Name');=0A= theForm.lastName.focus();=0A= return(false);=0A= } else if (theForm.firstName.value =3D=3D null ||=0A= theForm.firstName.value.length =3D=3D 0 || = allBlanks(theForm.firstName.value)) {=0A= alert('First Name is missing');=0A= theForm.firstName.focus();=0A= return(false);=0A= } else if (!allLetters(theForm.firstName.value) ) {=0A= alert('Illegal character(s) in First Name');=0A= theForm.firstName.focus();=0A= return(false);=0A= } else if ( !validEmail(theForm.email.value)) {=0A= alert('Email address is missing or invalid');=0A= theForm.email.focus();=0A= return(false);=0A= } else if (!document.applets[0].acceptSid(theForm.sid.value)) {=0A= alert('This SID is not enrolled.\nDid you set the course = correctly?');=0A= theForm.sid.focus();=0A= return(false);=0A= } else if (!validSID(theForm.sid.value)) {=0A= alert('Invalid password');=0A= theForm.sid.focus();=0A= return(false);=0A= } else if = (!document.applets[0].isOkPasswd(trimBlanks(theForm.sid.value),=0A= trimBlanks(theForm.email.value))) {=0A= alert('This email address is not enrolled, or does not match the = SID.\n' +=0A= 'Did you set the course correctly?');=0A= theForm.email.focus();=0A= return(false);=0A= } else {=0A= theForm.lastName.value =3D trimBlanks(theForm.lastName.value);=0A= theForm.firstName.value =3D trimBlanks(theForm.firstName.value);=0A= theForm.email.value =3D trimBlanks(theForm.email.value);=0A= theForm.sid.value =3D trimBlanks(theForm.sid.value);=0A= return(true);=0A= }=0A= }=0A= =0A= function saveResponses(fname,theForm,saveAns) {=0A= if(setSubmitCookie(fname,theForm,false)) {=0A= confirm('Your answers have been saved as a cookie on your = computer.\n' +=0A= 'Cookies are NOT RELIABLE storage--do not count on = them!\n' +=0A= 'You should write your answers down, too.\n' +=0A= 'The cookie will be erased automatically in ' + =0A= cookieExpireDays.toString() + ' days.');=0A= return(true);=0A= } else {=0A= alert('Error #1 in irGrade.saveResponses:\nYour answers have NOT = been saved!\n' +=0A= 'Something went wrong.');=0A= return(false);=0A= }=0A= }=0A= =0A= function setSubmitCookie(fff,theForm,idInfo){=0A= var s =3D collectResponses(theForm,false,idInfo);=0A= document.cookie =3D crypt(fff + theForm.sid.value, = theForm.sid.value) +=0A= "=3D" + crypt(s, theForm.sid.value) + ";EXPIRES=3D" + = expireTimeString();=0A= return(true);=0A= }=0A= =0A= function recoverResponses() {=0A= if (continueLab =3D=3D null) {=0A= return(false);=0A= } else {=0A= var theSid =3D getCookieVal(continueLab,"sid");=0A= var thePw =3D theSid;=0A= var tv =3D false;=0A= var theForm =3D document.forms[0];=0A= var ascStr =3D crypt(setNum.toString() + theSid, thePw)+ "=3D";=0A= var searchStr =3D document.cookie;=0A= var startInx =3D searchStr.indexOf(ascStr);=0A= if (startInx < 0 ) {=0A= return(false);=0A= }=0A= searchStr =3D = searchStr.substring(startInx+ascStr.length,searchStr.length);=0A= var endInx =3D searchStr.indexOf(";");=0A= if (endInx > -1 ) {=0A= searchStr =3D searchStr.substring(0,endInx);=0A= }=0A= searchStr =3D crypt(searchStr,thePw) + "&";=0A= var qName;=0A= var aText;=0A= var inx;=0A= var ampInx;=0A= var elem;=0A= for (var i=3D0; i < theForm.elements.length; i++) {=0A= qName =3D theForm.elements[i].name + '=3D';=0A= if (qName.indexOf("Q") =3D=3D 0) {=0A= elem =3D theForm.elements[i];=0A= if (elem.type =3D=3D "select-multiple") {=0A= while (searchStr.indexOf(qName) > -1) {=0A= inx =3D searchStr.indexOf(qName);=0A= searchStr =3D = searchStr.substring(inx+qName.length,searchStr.length);=0A= ampInx =3D searchStr.indexOf('&');=0A= qText =3D = unescape(searchStr.substring(0,ampInx));=0A= // search for option to select=0A= var ag =3D false;=0A= for (var j=3D0; j < elem.length; j++) {=0A= if (elem[j].value =3D=3D qText) {=0A= elem.options[j].selected =3D true;=0A= ag =3D true;=0A= }=0A= }=0A= }=0A= // if (CA && ag){=0A= //tv =3D checkAnswer(qName.substr(0,qName.length = - 1),=0A= // parseMultiple(theForm.elements[i].options));=0A= //}=0A= } else if (elem.type =3D=3D 'select-one') {=0A= inx =3D searchStr.indexOf(qName);=0A= if (inx > -1){=0A= searchStr =3D = searchStr.substring(inx+qName.length,searchStr.length);=0A= ampInx =3D searchStr.indexOf('&');=0A= qText =3D = unescape(searchStr.substring(0,ampInx));=0A= // search for option to select=0A= for (var j=3D0; j < elem.length; j++) {=0A= if (elem[j].value =3D=3D qText) {=0A= elem.options[j].selected =3D true;=0A= }=0A= }=0A= }=0A= // if (CA) {=0A= // var si =3D = theForm.elements[i].options.selectedIndex;=0A= // if (si !=3D null) {=0A= // tv =3D = checkAnswer(qName.substr(0,qName.length - 1),=0A= // elem.options[si].value);=0A= // }=0A= //}=0A= } else if (elem.type =3D=3D 'text') {=0A= inx =3D searchStr.indexOf(qName);=0A= if (inx > -1) {=0A= searchStr =3D searchStr.substring(=0A= inx+qName.length,searchStr.length);=0A= ampInx =3D searchStr.indexOf('&');=0A= qText =3D = unescape(searchStr.substring(0,ampInx));=0A= elem.value =3D qText;=0A= }=0A= // if (CA) {=0A= // var dba =3D trimBlanks(elem.value);=0A= // if (dba.length > 0) {=0A= // tv =3D = checkAnswer(qName.substr(0,qName.length - 1),=0A= // elem.value);=0A= // }=0A= //}=0A= } else if (elem.type =3D=3D null || elem.type =3D=3D = 'radio' || =0A= elem.type =3D=3D 'undefined') {=0A= inx =3D searchStr.indexOf(qName);=0A= if (inx > -1){=0A= searchStr =3D = searchStr.substring(inx+qName.length,searchStr.length);=0A= ampInx =3D searchStr.indexOf('&');=0A= qText =3D = unescape(searchStr.substring(0,ampInx));=0A= if (elem.value =3D=3D qText) {=0A= elem.checked =3D true;=0A= }=0A= }=0A= } else {=0A= alert('Error #1 in irGrade.recoverResponses(): = unsupported problem type ' +=0A= elem.type + '!');=0A= return(false);=0A= }=0A= }=0A= }=0A= }=0A= return(true);=0A= }=0A= =0A= function collectResponses(theForm,saveAs,saveId) {=0A= var typ;=0A= var nam;=0A= var s =3D '';=0A= s +=3D 'randSeed=3D' + escape(randSeed) + '&';=0A= for (var i=3D0; i < theForm.elements.length; i++) {=0A= typ =3D theForm.elements[i].type;=0A= nam =3D theForm.elements[i].name;=0A= if (typ =3D=3D "button" || typ =3D=3D "submit" || typ =3D=3D = "reset") {=0A= } else if (!saveId && (nam =3D=3D "lastName" || nam =3D=3D = "firstName" ||=0A= nam =3D=3D "sid" || nam =3D=3D "sid2" || = nam =3D=3D "email" ||=0A= nam =3D=3D "passwd" || nam =3D=3D = "passwd2")) {=0A= } else if (typ =3D=3D "select-one") {=0A= s +=3D escape(nam) + "=3D" +=0A= escape(theForm.elements[i].options[=0A= theForm.elements[i].options.selectedIndex].value)+ = "&";=0A= } else if (typ =3D=3D "select-multiple") {=0A= for (var j=3D0; j < theForm.elements[i].options.length; j++) = {=0A= if (theForm.elements[i].options[j].selected) {=0A= s +=3D escape(nam) + "=3D" +=0A= escape(theForm.elements[i].options[j].value) + = "&";=0A= }=0A= }=0A= } else if (typ =3D=3D "radio") {=0A= if (theForm.elements[i].checked) {=0A= s +=3D escape(nam) + '=3D' +=0A= escape(theForm.elements[i].value) + '&';=0A= }=0A= } else {=0A= s +=3D escape(nam) + "=3D" + = escape(theForm.elements[i].value) + "&";=0A= }=0A= }=0A= if (saveAs) {=0A= for (var i=3D0; i < key.length; i++) {=0A= s +=3D escape('a' + (i+1).toString()) + '=3D' + = escape(key[i].toString()) + '&';=0A= }=0A= }=0A= if (s[s.length-1] =3D=3D "&") {=0A= s =3D s.substring(0,s.length - 1);=0A= }=0A= return(s);=0A= }=0A= =0A= function labSetUp(seed, sn) {=0A= isLab =3D true;=0A= sectionContext =3D 'function setSectionContext() { \n' =0A= window.name=3D 'seti';=0A= setNum =3D sn;=0A= HI =3D true;=0A= if (typeof(parent.reveal) =3D=3D 'undefined') {=0A= CA =3D 'invalid';=0A= } else {=0A= CA =3D parent.reveal;=0A= }=0A= if (seed !=3D "SeEd") {=0A= rand =3D new rng(parseInt(seed));=0A= } else {=0A= continueLab =3D parent.continueLab;=0A= if (continueLab =3D=3D null || CA =3D=3D 'invalid') {=0A= alert('Error #1 in irGrade.labSetUp()!\n' +=0A= 'Problem Set not initialized correctly.\n' +=0A= 'You must use the Problem Set Form to go to this = page.\n' +=0A= 'If you did, make sure your browser is configured to = accept cookies, ' +=0A= ' and try again.\n ');=0A= document.close();=0A= window.close();=0A= return(false);=0A= } else {=0A= var searchStr =3D continueLab + '&';=0A= var pat =3D "randSeed=3D";=0A= var inx =3D searchStr.indexOf(pat);=0A= if (inx < 0) {=0A= alert('Error #2 in irGrade.labSetUp()!\n' +=0A= 'Problem Set not recovered correctly.\n' +=0A= 'Questions may have changed!');=0A= rand =3D new rng();=0A= } else {=0A= searchStr =3D searchStr.substring(=0A= inx + pat.length, searchStr.length);=0A= randSeed =3D = unescape(searchStr.substring(0,searchStr.indexOf('&')));=0A= rand =3D new rng(randSeed);=0A= }=0A= }=0A= }=0A= randSeed =3D rand.getSeed();=0A= writeProblemSetHeader(setNum);=0A= return(true);=0A= }=0A= =0A= function setRequiredInputs(theForm) {=0A= theForm.elements['lastName'].value =3D = getCookieVal(continueLab,"lastName");=0A= theForm.elements['firstName'].value =3D = getCookieVal(continueLab,"firstName");=0A= theForm.elements['email'].value =3D = getCookieVal(continueLab,"email");=0A= theForm.elements['sid'].value =3D getCookieVal(continueLab,"sid");=0A= theForm.elements['sid2'].value =3D getCookieVal(continueLab,"sid");=0A= theForm.elements['passwd'].value =3D getCookieVal(continueLab,"sid");=0A= theForm.elements['passwd2'].value =3D = getCookieVal(continueLab,"sid");=0A= return(true);=0A= }=0A= =0A= function setExtraInputs(theForm) {=0A= theForm.elements['inlinekey'].value =3D inlinePrefix + = (qCtr-1).toString();=0A= theForm.elements['dFile'].value =3D parent.dFile;=0A= theForm.elements['teacher'].value =3D parent.teacher;=0A= theForm.elements['class'].value =3D parent.course;=0A= theForm.elements['extrainfo'].value =3D escape("seed=3D" + = randSeed.toString() +=0A= "&irGradeVersion=3D" + irGradeModTime.toString());=0A= var nRight =3D 0;=0A= var qVal;=0A= var resp;=0A= var qType;=0A= for (var i=3D1; i < qCtr; i++) {=0A= qVal =3D 'Q' + i.toString();=0A= qType =3D theForm.elements[qVal].type;=0A= if (qType =3D=3D 'select-one') {=0A= resp =3D theForm.elements[qVal].options[=0A= theForm.elements[qVal].options.selectedIndex].value;=0A= } else if (qType =3D=3D 'select-multiple') {=0A= resp =3D parseMultiple(theForm.elements[qVal].options);=0A= } else if (qType =3D=3D 'text') {=0A= resp =3D theForm.elements[qVal].value;=0A= } else if (qType =3D=3D 'radio') {=0A= if (theForm.elements[qVal].checked) {=0A= resp =3D theForm.elements[qVal].value;=0A= }=0A= } else if (qType =3D=3D null || qType =3D=3D 'undefined') { // = radio too!=0A= if (theForm.elements[qVal].checked) {=0A= resp =3D theForm.elements[qVal].value;=0A= }=0A= } else {=0A= alert('Error #1 in irGrade.setExtraInputs(): Input type ' + = qType +=0A= ' in question ' + qVal + ' is not supported!');=0A= }=0A= if (scoreProblem(key[i-1],resp)) nRight++;=0A= }=0A= theForm.elements['score'].value =3D roundToDig(100*nRight/(qCtr - = 1),2).toString();=0A= return(true);=0A= }=0A= =0A= function killApplets() { // dispose of applets when leaving the page=0A= for (var i =3D 0; i < document.applets.length; i++) {=0A= document.applets[i].stop();=0A= document.applets[i].destroy();=0A= }=0A= return(true);=0A= }=0A= =0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D SPECIAL HTML GENERATORS = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= =0A= function chapterSetUp(seed, chNum, titStr) {=0A= theChapter =3D null;=0A= for (var i=3D0; i < theChapters.length; i++) {=0A= if (theChapters[i].toString() =3D=3D chNum.toString()) {=0A= theChapter =3D i;=0A= }=0A= }=0A= if (theChapter =3D=3D null) {=0A= alert('Error in irGrade.chapterSetUp(): chapter ' + chNum +=0A= ' is not in the index!');=0A= theChapter =3D 0;=0A= }=0A= var statStr;=0A= if (seed !=3D "SeEd") {=0A= rand =3D new rng(parseInt(seed));=0A= } else {=0A= rand =3D new rng();=0A= }=0A= window.name =3D "bookWin";=0A= if (typeof(titStr) =3D=3D 'undefined' || titStr =3D=3D null ) {=0A= statStr =3D "Chapter " + (theChapters[theChapter]).toString();=0A= } else {=0A= statStr =3D titStr;=0A= }=0A= defaultStatus =3D "SticiGui " + statStr;=0A= document.writeln('' + defaultStatus + '' +=0A= '');=0A= document.writeln("

SticiGui " + statStr + "

");=0A= CA =3D (1=3D=3D1);=0A= HI =3D false;=0A= randSeed =3D rand.getSeed();=0A= sectionContext =3D 'function setSectionContext() { \n' =0A= return(true);=0A= }=0A= =0A= function examSetUp(seed, sName, sn) {=0A= isLab =3D false;=0A= sectionContext =3D 'function setSectionContext() { \n' =0A= window.name=3D 'seti';=0A= examName =3D sName;=0A= examNum =3D sn;=0A= HI =3D true;=0A= if (seed !=3D "SeEd") {=0A= rand =3D new rng(parseInt(seed));=0A= } else {=0A= rand =3D new rng();=0A= }=0A= randSeed =3D rand.getSeed();=0A= writeExamHeader(examName, examNum.toString() + '.' + = randSeed.toString() );=0A= defaultStatus =3D 'SticiGui ' + examName + ' ' + examNum.toString();=0A= return(true);=0A= }=0A= =0A= function writeExamHeader(exNam, exVer) {=0A= document.writeln("

");=0A= document.writeln("

" +=0A= "SticiGui " + exNam + '

Version ' = + =0A= exVer.toString() + '

');=0A= return(true);=0A= }=0A= =0A= function setApplets() {=0A= if ( (typeof (document.forms) !=3D 'undefined') && (document.forms = !=3D null) &&=0A= (document.forms.length > 0 ) && !isLab ) {=0A= sectionContext +=3D 'document.forms[0].reset();\n';=0A= }=0A= if (isLab) {=0A= sectionContext +=3D 'recoverResponses();\n';=0A= }=0A= sectionContext +=3D '}';=0A= eval(sectionContext);=0A= setSectionContext();=0A= }=0A= =0A= function writeProblemSetFooter() {=0A= document.writeln('

');=0A= if (parent.allowSubmit) {=0A= document.writeln('');=0A= document.writeln(' = ');=0A= } else {=0A= document.writeln(' ');=0A= }=0A= document.writeln('

');=0A= document.writeln('

');=0A= printFootnotes();=0A= writeMiscFooter(false);=0A= return(true);=0A= }=0A= =0A= function writeSolution(p,text,evalStr) {=0A= longKey[p-1] =3D text;=0A= solutionCode[p-1] =3D evalStr;=0A= document.writeln('
Solution.');=0A= return(true);=0A= }=0A= =0A= function writeFootnote(p,label,text) {=0A= footnotes[p] =3D text;=0A= document.writeln('^{' + label.toString() + '}');=0A= return(true);=0A= }=0A= =0A= function printFootnotes() {=0A= if (footnotes.length > 0) {=0A= document.writeln('

' +=0A= 'Footnotes

');=0A= for (var i=3D0; i < footnotes.length; i++ ) {=0A= if (typeof(footnotes[i]) !=3D 'undefined') {=0A= document.writeln('

' +=0A= 'Footnote ' + (i+1).toString() + '. ' = +=0A= footnotes[i] + '

');=0A= }=0A= }=0A= }=0A= }=0A= =0A= function writeChapterFooter() {=0A= printFootnotes();=0A= if (longKey.length > 0 ) {=0A= document.writeln('

' +=0A= 'Solutions to Selected Exercises

');=0A= for (var i=3D0; i < longKey.length; i++ ) {=0A= if (typeof(longKey[i]) !=3D 'undefined') {=0A= document.writeln('

' +=0A= 'Solution to exercise ' + (i+1).toString() + = '. ' +=0A= longKey[i] + '

');=0A= }=0A= if (typeof(solutionCode[i]) !=3D 'undefined' && = solutionCode[i] !=3D null=0A= && solutionCode[i] !=3D "") {=0A= eval(solutionCode[i]);=0A= }=0A= }=0A= }=0A= document.writeln('

');=0A= if (theChapter > 1) {=0A= document.writeln('Chapter ' + = (theChapters[theChapter-1]).toString() + =0A= ' (previous) | ') ;=0A= }=0A= document.writeln('Chapter ' + theChapters[theChapter] + ' = (current) ');=0A= if (theChapter < theChapters.length - 1) {=0A= document.writeln(' | ' +=0A= 'Chapter ' + = (theChapters[theChapter+1]).toString() + =0A= ' (next)
') ;=0A= }=0A= document.writeln('' +=0A= 'Text Table of Contents
' +=0A= '' +=0A= 'Problem Sets
' +=0A= '' +=0A= 'Glossary
' +=0A= '' +=0A= 'SticiGui Home

');=0A= writeMiscFooter(false);=0A= return(true);=0A= }=0A= =0A= function writeMiscFooter(sr) {=0A= var stra =3D '

' +=0A= 'SticiGui Home

';=0A= if (typeof(sr) =3D=3D 'boolean') {=0A= if (sr) {=0A= document.writeln(stra + '..' + strb);=0A= }=0A= } else {=0A= document.writeln(stra + sr + strb);=0A= }=0A= document.write('

©' + copyYr + = pbsRef +=0A= '. All rights reserved.
Last generated = ' + today +=0A= '. ');=0A= if ( !(typeof(pageModDate) =3D=3D 'undefined') && !(pageModDate = =3D=3D null) ) {=0A= document.write('Content last modified ' + pageModDate + '. ');=0A= }=0A= document.writeln('

');=0A= return(true);=0A= }=0A= =0A= function writeProblemSetHeader(sn) {=0A= document.writeln("

");=0A= var formName =3D "SticiGuiSet" + sn.toString();=0A= document.writeln("");=0A= continueLab =3D parent.continueLab;=0A= if (continueLab =3D=3D null) {=0A= alert('Error #1 in irGrade.writeProblemSetHeader()!\n' +=0A= 'The problem set is not correctly initialized.\n' +=0A= 'Make sure your browser is set up to accept cookies and try = again.');=0A= document.close();=0A= window.close();=0A= return(false);=0A= } else {=0A= document.writeln("" +=0A= " " +=0A= " " +=0A= " " +=0A= " " +=0A= " " = +=0A= " ");=0A= }=0A= document.writeln("");=0A= document.writeln("");=0A= document.writeln("");=0A= document.writeln("");=0A= document.writeln("");=0A= document.writeln("");=0A= setRequiredInputs(document.forms[0]);=0A= document.writeln("

" +=0A= "SticiGui Problem Set "=0A= + sn.toString() + "

");=0A= return(true);=0A= }=0A= =0A= function makeOptions(ans, pert, dig, extra) { // make a set of numerical = options as answers,=0A= // converted to strings = with dig digits of=0A= // precision. each answer = is perturbed by a=0A= // signed multiple of pert.=0A= // extra is appended to = each answer=0A= if (typeof(dig) =3D=3D "undefined" || dig =3D=3D null) {=0A= dig =3D 0;=0A= }=0A= if (typeof(extra) =3D=3D "undefined" || extra =3D=3D null) {=0A= extra =3D "";=0A= }=0A= var rs =3D listOfRandSigns(5);=0A= var rawOpt =3D new Array(5);=0A= for (var i=3D0; i < 5; i++) {=0A= rawOpt[i] =3D commify(roundToDig(ans + i*rs[i]*pert,dig)) + = extra;=0A= }=0A= var optPerm =3D randPermutation(rawOpt,"inverse");=0A= optPerm[1] =3D alphabet[optPerm[1][0]];=0A= return(optPerm);=0A= }=0A= =0A= function makeRangeOptions(t, lo, hi, loLim, hiLim, dig, extra, iterLim) = { =0A= // make multiple choice options=0A= // t is truth, lo is starting lower limit, hi is starting = upper limit,=0A= // loLim is ultimate lower limit, hiLim is ultimate upper = limit,=0A= // dig is digits of precision, extra is appended to each = answer=0A= // steps up and down by 10% until t is within 0.3 of the = space between=0A= // answers of one of the answers=0A= var pertFac =3D 0.07; // amount by which to move endpoints each = iteration=0A= var closeFac =3D 0.35; // how much closer should answer be to = one endpoint?=0A= var av;=0A= var altern =3D false; // alternate moving upper and lower = endpoints=0A= if (typeof(extra) =3D=3D 'undefined' || extra =3D=3D null) {=0A= extra =3D "";=0A= }=0A= if (typeof(dig) =3D=3D 'undefined' || dig =3D=3D null) {=0A= dig =3D 2;=0A= }=0A= var ok =3D false;=0A= var lim =3D 0;=0A= var maxIt;=0A= if (typeof(iterLim) =3D=3D 'undefined' || iterLim =3D=3D null) {=0A= maxIt =3D maxIterations;=0A= } else {=0A= maxIt =3D iterLim;=0A= }=0A= while(!ok && lim <=3D maxIt) {=0A= var ans =3D linspace(lo,hi,5);=0A= var d =3D closeFac*(ans[1]-ans[0]); // want to be = significantly closer to one end=0A= if (t <=3D ans[0] ) {=0A= av =3D alphabet[0];=0A= ok =3D true;=0A= } else if ( t >=3D ans[4]) {=0A= av =3D alphabet[4];=0A= ok =3D true;=0A= } else {=0A= for (i=3D0; i < ans.length; i++) {=0A= if (Math.abs(t - ans[i]) <=3D d) {=0A= ok =3D true;=0A= av =3D alphabet[i];=0A= }=0A= }=0A= if (altern) {=0A= lo =3D loLim + (1.0 - pertFac)*(lo-loLim);=0A= altern =3D !altern;=0A= } else {=0A= hi =3D hi + pertFac*(hiLim-hi);=0A= altern =3D !altern;=0A= }=0A= }=0A= if (lim++ =3D=3D maxIt) {=0A= av =3D alphabet[0];=0A= var ref =3D Math.abs(t-ans[0]);=0A= for (var i=3D1; i < ans.length; i++ ) {=0A= var nref =3D Math.abs(t-ans[i]);=0A= if (nref < ref) {=0A= ref =3D nref;=0A= av =3D alphabet[i];=0A= }=0A= }=0A= ok =3D true;=0A= alert('Error #1 in irGrade.makeRangeOptions: maximum = iterations exceeded in ' +=0A= 'problem ' + (pCtr-1).toString() + '.\nPlease report = this to your ' +=0A= 'instructor.');=0A= }=0A= }=0A= var opt =3D new Array(ans.length);=0A= for (i=3D0; i < ans.length; i++) {=0A= opt[i] =3D (roundToDig(ans[i],dig)).toString()+ extra;=0A= }=0A= var out =3D new Array(2);=0A= out[0] =3D opt;=0A= out[1] =3D av;=0A= return(out);=0A= }=0A= =0A= function makeProbOptions(t, lo, hi, dig, iter) {=0A= if (typeof(dig) =3D=3D 'undefined' || dig =3D=3D null) {=0A= dig =3D 0;=0A= }=0A= return(makeRangeOptions(100*t,100*lo,100*hi,0,100,dig,'%', iter));=0A= }=0A= =0A= function truthTable(title, valArr) { // make a 2 by 2 truth table=0A= if (valArr.length < 4) {=0A= alert('Error #1 in irGrade.truthTable: number of truth values is = ' + valArr.length);=0A= return(null);=0A= } else {=0A= return(truthTableHeader(title) +=0A= valArr[0] + '' +=0A= valArr[1] +=0A= 'F' +=0A= '' +=0A= valArr[2] + '' +=0A= valArr[3] + '

'=0A= );=0A= }=0A= }=0A= =0A= function writeTruthTable(title, valArr) {=0A= document.writeln(truthTable(title, valArr));=0A= return(true);=0A= }=0A= =0A= function truthTableHeader(title) {=0A= return( '

' +=0A= '' +=0A= '' +=0A= '' +=0A= '' = +=0A= '' +=0A= '' +=0A= '' +=0A= '

Truth table for ' +=0A= title + '
	p	T	F
q
T		');=0A= }=0A= =0A= function writeTruthTableProblem(title, ansArr) { // 2 by 2 truth table = problem=0A= var opt =3D ['T','F'];=0A= document.writeln(truthTableHeader(title));=0A= var solArr =3D new Array(ansArr.length);=0A= if ( (typeof(ansArr)).toLowerCase() =3D=3D 'function') {=0A= trueArr =3D [true, false];=0A= for (var i=3D0; i < 2; i++ ) {=0A= for (var j=3D0; j < 2; j++) {=0A= var inx =3D j + 2*i;=0A= if (ansArr(trueArr[j], trueArr[i])) {=0A= solArr[inx] =3D 'a';=0A= } else {=0A= solArr[inx] =3D 'b';=0A= }=0A= }=0A= }=0A= } else {=0A= for (var i=3D0; i < ansArr.length; i++) {=0A= if (ansArr[i]) {=0A= solArr[i] =3D 'a';=0A= } else {=0A= solArr[i] =3D 'b';=0A= }=0A= }=0A= }=0A= writeSelectExercise(false,qCtr++,opt,solArr[0]);=0A= document.writeln('	');=0A= writeSelectExercise(false,qCtr++,opt,solArr[1]);=0A= document.writeln('
F		');=0A= writeSelectExercise(false,qCtr++,opt,solArr[2]);=0A= document.writeln('	');=0A= writeSelectExercise(false,qCtr++,opt,solArr[3]);=0A= document.writeln('

');=0A= }=0A= =0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= // =3D=3D=3Dformatting functions and html generators=3D=3D=3D=3D=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=0A= =0A= =0A= function commify(num) { // punctuate number strings greater than 1,000 = in magnitude=0A= var str;=0A= var strA =3D (removeAllBlanks(num.toString())).toLowerCase();=0A= if ( (strA.indexOf('e') > -1) || (strA.indexOf('d') > -1) ) {=0A= str =3D strA; // don't mess with exponential notation=0A= } else {=0A= str =3D strA;=0A= var curLoc =3D str.length;=0A= if ( str.indexOf('.') > -1 ) {=0A= curLoc =3D str.indexOf('.');=0A= }=0A= var negSign =3D str.indexOf('-');=0A= for (var loc =3D curLoc-4; loc > negSign; loc -=3D 3) {=0A= str =3D str.substr(0,loc+1) + ',' + str.substr(loc+1, = str.length);=0A= }=0A= }=0A= return(str);=0A= }=0A= =0A= =0A= =0A= function writeBlankLines(k) { // blank space=0A= if ( (typeof(k) =3D=3D 'undefined') || (k =3D=3D null) || (k < 0) ) {=0A= k =3D 1;=0A= }=0A= for (var i=3D0; i < k; i++) {=0A= document.writeln('

');=0A= }=0A= }=0A= =0A= function roundToDig(num,dig) { // rounds a number to dig digits after = the decimal place=0A= var powOfTen =3D Math.pow(10,dig);=0A= var fmt =3D Math.round(num*powOfTen)/powOfTen;=0A= return(fmt);=0A= }=0A= =0A= function doubleToStr(num,dig) {=0A= // returns a string representation of num, rounded to dig digits after = the decimal=0A= return(removeAllBlanks(roundToDig(num,dig).toString()));=0A= }=0A= =0A= function doubleToRange(num,fudge) {=0A= // returns a string range of num +/- fudge, separated by a colon=0A= var dig =3D -Math.floor(Math.log(Math.abs(fudge))/Math.log(10)) + 1;=0A= var s =3D roundToDig(num,dig);=0A= var range =3D doubleToStr(s - Math.abs(fudge),dig) + ":" +=0A= doubleToStr(s+ Math.abs(fudge),dig);=0A= range =3D range.replace(/ /g,'');=0A= return(range);=0A= }=0A= =0A= function numToRange(num,fudge) {=0A= // returns a string range of num +/- fudge, separated by a colon=0A= if ( (typeof(fudge) =3D=3D 'undefined') || (fudge =3D=3D null) ) {=0A= fudge =3D fudgeFactor*num;=0A= }=0A= if (fudge =3D=3D 0) {=0A= fudge =3D absFudge;=0A= }=0A= return(doubleToRange(num,Math.abs(fudge)));=0A= }=0A= =0A= function numToOrdinal(num) { // turns integer into string, appends = appropriate suffix=0A= var st =3D (roundToDig(num,0)).toString();=0A= var suffArray =3D = ["th","st","nd","rd","th","th","th","th","th","th"];=0A= var finalDig =3D parseInt(st.substr(st.length-1,st.length));=0A= return(st + suffArray[finalDig]);=0A= }=0A= =0A= function listToTable(header,list,orientation,centering,print,ft) {=0A= // formats an array of arrays as an html table=0A= if (typeof(centering) =3D=3D 'undefined' || centering =3D=3D null) {=0A= centering =3D "right";=0A= }=0A= if (typeof(print) =3D=3D 'undefined') {=0A= print =3D true;=0A= }=0A= if (typeof(ft) =3D=3D 'undefined' || ft =3D=3D null) {=0A= ft =3D "";=0A= eft =3D "";=0A= } else {=0A= ft =3D '';=0A= eft =3D '';=0A= }=0A= var rows =3D list.length;=0A= var cols;=0A= if (typeof(list[0]) !=3D 'object') {=0A= cols=3Dnull;=0A= } else {=0A= cols =3D list[0].length;=0A= }=0A= var str =3D "

";=0A= if (cols =3D=3D null || cols =3D=3D 1) {=0A= str +=3D"";=0A= str +=3D"\n";=0A= if (orientation =3D=3D "standard") {=0A= for (var j=3D0; j < rows; j++) {=0A= str +=3D"\n";=0A= }=0A= str +=3D"";=0A= } else if (orientation =3D=3D "transpose") {=0A= str +=3D"";=0A= for (var j=3D0; j < rows; j++) {=0A= str +=3D"";=0A= str +=3D"\n";=0A= str +=3D"";=0A= }=0A= } else {=0A= alert("Error 1 in irGrade.listToTable: unsupported = orientation " + orientation);=0A= }=0A= } else {=0A= if (orientation =3D=3D "standard") {=0A= for (var j =3D 0; j < rows; j++) {=0A= str +=3D "";=0A= str +=3D "\n";=0A= for (var i=3D0; i < cols; i++) {=0A= str +=3D "";=0A= }=0A= str +=3D"";=0A= }=0A= } else if (orientation =3D=3D "transpose") {=0A= str +=3D "";=0A= for (var i=3D0; i < header.length; i++) {=0A= str +=3D "\n";=0A= }=0A= str +=3D "";=0A= for (var j =3D 0; j < cols; j++) {=0A= str +=3D "";=0A= for (var i=3D0; i < rows; i++) {=0A= str +=3D "\n";=0A= }=0A= str +=3D"";=0A= }=0A= } else {=0A= alert("Error 2 in irGrade.listToTable: unsupported = orientation " + orientation);=0A= }=0A= }=0A= str +=3D "

" + ft + header +eft = + "	" + ft + = list[j] + eft + "
" + ft + = list[j] + eft + "
" + ft + = header[j] + eft + "	" +=0A= ft + list[j][i] + eft + "
" + ft + = header[i] + eft + "
" + ft + = list[i][j] + eft + "

";=0A= if (print) {=0A= document.writeln(str);=0A= return(true);=0A= } else {=0A= return(str);=0A= }=0A= }=0A= =0A= function arrayToRow(v,alignment) {=0A= // makes a row of a table from the elements of the array v, with = specified alignment=0A= document.writeln("");=0A= for (var i=3D0; i < v.length; i++) {=0A= document.write('');=0A= document.write(v[i].toString());=0A= document.writeln("");=0A= }=0A= document.writeln("");=0A= return(true);=0A= }=0A= =0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=0A= // = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= STATISTICAL SUBROUTINES = =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=0A= =0A= function mean(list) { // computes the mean of the list=0A= return(vSum(list)/list.length);=0A= }=0A= =0A= function vMult(a, list) { // multiply a vector times a scalar=0A= var list2 =3D new Array(list.length);=0A= for (var i=3D0; i < list.length; i++) {=0A= list2[i] =3D a*list[i];=0A= }=0A= return(list2);=0A= }=0A= =0A= function vPointwiseMult(list1, list2) { // componentwise multiplication = of two vectors=0A= var list3 =3D Math.NaN;=0A= if (list1.length !=3D list2.length) {=0A= alert('Error #1 in irGrade.vPointwiseMult: vector lengths do not = match!');=0A= } else {=0A= list3 =3D new Array(list1.length);=0A= for (var i=3D0; i < list1.length; i++) {=0A= list3[i] =3D list1[i]*list2[i];=0A= }=0A= }=0A= return(list3);=0A= }=0A= =0A= function vFloor(list) { // takes floor of all components=0A= var list2 =3D new Array(list.length);=0A= for (var i =3D 0; i < list.length; i++) {=0A= list2[i] =3D Math.floor(list[i]);=0A= }=0A= return(list2);=0A= }=0A= =0A= function vCeil(list) { // takes ceil of all components=0A= var list2 =3D new Array(list.length);=0A= for (var i =3D 0; i < list.length; i++) {=0A= list2[i] =3D Math.ceil(list[i]);=0A= }=0A= return(list2);=0A= }=0A= =0A= function vRoundToInts(list) { // round all components to the nearest int=0A= var list2 =3D new Array(list.length);=0A= var tmp;=0A= for (var i =3D 0; i < list.length; i++) {=0A= list2[i] =3D Math.floor(list[i]);=0A= if (list[i] - list2[i] >=3D 0.5) {=0A= list2[i]++;=0A= }=0A= }=0A= return(list2);=0A= }=0A= =0A= function vSum(list) { // computes the sum of the elements of list=0A= var tot =3D 0.0;=0A= for (var i =3D 0; i < list.length; i++) {=0A= tot +=3D list[i];=0A= }=0A= return(tot);=0A= }=0A= =0A= function vCum(list) { // vector of cumulative sum=0A= var list2 =3D list;=0A= for (var i =3D 1; i < list.length; i++ ) {=0A= list2[i] +=3D list2[i-1];=0A= }=0A= return(list2);=0A= }=0A= =0A= function vZero(n) { // returns a vector of zeros of length n=0A= var list =3D new Array(n);=0A= for (var i=3D0; i < n; i++) {=0A= list[i] =3D 0.0;=0A= }=0A= return(list);=0A= }=0A= =0A= function vOne(n) { // returns a vector of ones of length n=0A= var list =3D new Array(n);=0A= for (var i=3D0; i < n; i++) {=0A= list[i] =3D 1.0;=0A= }=0A= return(list);=0A= }=0A= =0A= function twoNorm(list) { // two norm of a vector=0A= var tn =3D 0.0;=0A= for (var i=3D0; i < list.length; i++) {=0A= tn +=3D list[i]*list[i];=0A= }=0A= return(Math.sqrt(tn));=0A= }=0A= =0A= function convolve(a,b) { // convolve two lists=0A= var c =3D new Array(a.length + b.length - 1);=0A= var left; var right;=0A= for (var i=3D0; i < a.length + b.length - 1; i++) {=0A= c[i] =3D 0;=0A= right =3D Math.min(i+1, a.length);=0A= left =3D Math.max(0, i - b.length + 1);=0A= for (var j=3Dleft; j < right; j++) {=0A= c[i] +=3D a[j]*b[b.length - i - 1 + j];=0A= }=0A= }=0A= return(c);=0A= }=0A= =0A= function nFoldConvolve(a,n) {=0A= var b =3D a;=0A= for (var i=3D0; i < n; i++ ) {=0A= b =3D convolve(b,a);=0A= }=0A= return(b);=0A= }=0A= =0A= function numberLessThan(a,b) { // numerical ordering for javascript sort = function=0A= var diff =3D parseFloat(a)-parseFloat(b);=0A= if (diff < 0) {=0A= return(-1);=0A= } else if (diff =3D=3D 0) {=0A= return(0);=0A= } else {=0A= return(1);=0A= }=0A= }=0A= =0A= function numberGreaterThan(a,b) { // numerical ordering for javascript = sort function=0A= var diff =3D parseFloat(a)-parseFloat(b);=0A= if (diff < 0) {=0A= return(1);=0A= } else if (diff =3D=3D 0) {=0A= return(0);=0A= } else {=0A= return(-1);=0A= }=0A= }=0A= =0A= function sd(list) { // computes the SD of the list=0A= ave =3D mean(list);=0A= ssq =3D 0;=0A= for (var i =3D 0; i < list.length; i++) {=0A= ssq +=3D (list[i] - ave)*(list[i] - ave);=0A= }=0A= ssq =3D Math.sqrt(ssq/list.length);=0A= return(ssq);=0A= }=0A= =0A= function sampleSd(list) { // computes the sample SD of the list=0A= ave =3D mean(list);=0A= ssq =3D 0;=0A= for (var i =3D 0; i < list.length; i++) {=0A= ssq +=3D (list[i] - ave)*(list[i] - ave);=0A= }=0A= ssq =3D Math.sqrt(ssq/(list.length - 1.0));=0A= return(ssq);=0A= }=0A= =0A= function corr(list1, list2) {=0A= // computes the correlation coefficient of list1 and list2=0A= if (list1.length !=3D list2.length) {=0A= alert("Error #1 in irGrade.corr(): lists have different = lengths!");=0A= return(Math.NaN);=0A= } else {=0A= var ave1 =3D mean(list1);=0A= var ave2 =3D mean(list2);=0A= var sd1 =3D sd(list1);=0A= var sd2 =3D sd(list2);=0A= var cc =3D 0.0;=0A= for (var i=3D0; i < list1.length; i++) {=0A= cc +=3D (list1[i] - ave1)*(list2[i] - ave2);=0A= }=0A= cc /=3D sd1*sd2*list1.length;=0A= return(cc);=0A= }=0A= }=0A= =0A= function percentile(list,p) { // finds the pth percentile of list=0A= var n =3D list.length;=0A= var sList =3D new Array(n);=0A= for (var i=3D0; i < n; i++) sList[i] =3D list[i].valueOf();=0A= sList.sort(numberLessThan);=0A= var ppt =3D Math.max(Math.ceil(p*n/100),1);=0A= return(sList[ppt-1]);=0A= }=0A= =0A= function listOfRandSigns(n) { // random +-1 vector=0A= var list =3D new Array(n);=0A= for (var i=3D0; i < n; i++) {=0A= var rn =3D rand.next();=0A= if (rn < 0.5) {=0A= list[i] =3D -1;=0A= } else {=0A= list[i] =3D 1;=0A= }=0A= }=0A= return(list);=0A= }=0A= =0A= function listOfRandUniforms(n, lo, hi) { // n random variables uniform = on (lo, hi)=0A= if ( (typeof(lo) =3D=3D 'undefined') || (lo =3D=3D null) ) {=0A= lo =3D 0.0;=0A= }=0A= if ( (typeof(hi) =3D=3D 'undefined') || (hi =3D=3D null) ) {=0A= hi =3D 1.0;=0A= }=0A= var list =3D new Array(n);=0A= for (var i=3D0; i < n; i++) {=0A= list[i] =3D lo + (hi-lo)*rand.next();=0A= }=0A= return(list);=0A= }=0A= =0A= function listOfRandInts(n, lo, hi) { // n random integers between lo and = hi=0A= var list =3D new Array(n);=0A= for (var i=3D0; i < n; i++) {=0A= list[i] =3D Math.floor((hi+1 - lo)*rand.next()) + lo;=0A= }=0A= return(list);=0A= }=0A= =0A= function listOfDistinctRandInts(n, lo, hi) { // n dintinct random = integers between lo and hi=0A= var list =3D new Array(n);=0A= var trial;=0A= var i=3D0;=0A= var unique;=0A= while (i < n) {=0A= trial =3D Math.floor((hi+1 - lo)*rand.next()) + lo;=0A= unique =3D true;=0A= for (var j =3D 0; j < i; j++) {=0A= if (trial =3D=3D list[j]) unique =3D false;=0A= }=0A= if (unique) {=0A= list[i] =3D trial;=0A= i++;=0A= }=0A= }=0A= return(list);=0A= }=0A= =0A= function randomSample(list, ssize, replace) {=0A= // sample from list, size ssize w/ or w/o replacement.=0A= // default is without replacement=0A= var sample =3D new Array();=0A= var indices =3D new Array();=0A= if (replace !=3D null && replace ) {=0A= indices =3D listOfRandInts(ssize,0,list.length-1);=0A= } else {=0A= indices =3D listOfDistinctRandInts(ssize,0,list.length - 1);=0A= }=0A= for (var i=3D0; i < ssize; i++) {=0A= sample[i] =3D list[indices[i]];=0A= }=0A= return(sample) ;=0A= }=0A= =0A= function multinomialSample(pVec, n) { // multinomial sample of size n = with probabilities pVec=0A= pVec =3D vMult(1.0/vSum(pVec), pVec); // renormalize in case=0A= var pCum =3D vCum(pVec);=0A= var counts =3D vZero(pVec.length);=0A= var rv;=0A= var inx;=0A= for (var i=3D0; i < n; i++) {=0A= rv =3D rand.next();=0A= inx =3D 0;=0A= while ( (rv > pCum[inx]) && (inx < n) ) {=0A= inx++;=0A= }=0A= counts[inx]++;=0A= }=0A= return(counts);=0A= }=0A= =0A= function normPoints(n, mu, s, dig) { // n normals with expected value = mu, sd s, rounded to dig=0A= var round =3D true;=0A= if ( (typeof(dig) =3D=3D 'undefined') || (dig =3D=3D null) ) {=0A= var round =3D false;=0A= }=0A= var xVal =3D new Array(n);=0A= if (round) {=0A= for (var i=3D0; i < n; i++) {=0A= xVal[i] =3D roundToDig(mu + s*rNorm(),dig);=0A= }=0A= } else {=0A= for (var i=3D0; i < n; i++) {=0A= xVal[i] =3D mu + s*rNorm(),dig;=0A= }=0A= }=0A= return(xVal);=0A= }=0A= =0A= function cNormPoints(n, r) {=0A= // generate pseudorandom normal bivariate w/ specified realized = correlation coefficient=0A= var xVal =3D new Array(n);=0A= var yVal =3D new Array(n);=0A= for (var i=3D0; i 4.0=0A= var p =3D [3.05326634961232344e-1, 3.60344899949804439e-1,=0A= 1.25781726111229246e-1, 1.60837851487422766e-2,=0A= 6.58749161529837803e-4, 1.63153871373020978e-2];=0A= var q =3D [2.56852019228982242e00, 1.87295284992346047e00,=0A= 5.27905102951428412e-1, 6.05183413124413191e-2,=0A= 2.33520497626869185e-3];=0A= var y, z, xnum, xden, result, del;=0A= =0A= /*=0A= Translation of a FORTRAN program by W. J. Cody,=0A= Argonne National Laboratory, NETLIB/SPECFUN, March 19, 1990.=0A= The main computation evaluates near-minimax approximations=0A= from "Rational Chebyshev approximations for the error function"=0A= by W. J. Cody, Math. Comp., 1969, PP. 631-638.=0A= */=0A= =0A= // evaluate erf for |x| <=3D 0.46875=0A= =0A= if(Math.abs(x) <=3D xbreak) {=0A= y =3D Math.abs(x);=0A= z =3D y * y;=0A= xnum =3D a[4]*z;=0A= xden =3D z;=0A= for (var i =3D 0; i< 3; i++) {=0A= xnum =3D (xnum + a[i]) * z;=0A= xden =3D (xden + b[i]) * z;=0A= }=0A= result =3D 1.0 - x* (xnum + a[3])/ (xden + b[3]);=0A= } else if (Math.abs(x) <=3D 4.0) {=0A= y =3D Math.abs(x);=0A= xnum =3D c[8]*y;=0A= xden =3D y;=0A= for (var i =3D 0; i < 7; i++) {=0A= xnum =3D (xnum + c[i])* y;=0A= xden =3D (xden + d[i])* y;=0A= }=0A= result =3D (xnum + c[7])/(xden + d[7]);=0A= if (y > 0.0) {=0A= z =3D Math.floor(y*16)/16.0;=0A= } else {=0A= z =3D Math.ceil(y*16)/16.0;=0A= }=0A= del =3D (y-z)*(y+z);=0A= result =3D Math.exp(-z*z) * Math.exp(-del)* result;=0A= } else {=0A= y =3D Math.abs(x);=0A= z =3D 1.0 / (y*y);=0A= xnum =3D p[5]*z;=0A= xden =3D z;=0A= for (var i =3D 0; i < 4; i++) {=0A= xnum =3D (xnum + p[i])* z;=0A= xden =3D (xden + q[i])* z;=0A= }=0A= result =3D z * (xnum + p[4]) / (xden + q[4]);=0A= result =3D (1.0/Math.sqrt(Math.PI) - result)/y;=0A= if (y > 0.0) {=0A= z =3D Math.floor(y*16)/16.0;=0A= } else {=0A= z =3D Math.ceil(y*16)/16.0;=0A= }=0A= del =3D (y-z)*(y+z);=0A= result =3D Math.exp(-z*z) * Math.exp(-del) * result;=0A= }=0A= if (x < -xbreak) {=0A= result =3D 2.0 - result;=0A= }=0A= return(result);=0A= }=0A= =0A= function normInv(p) {=0A= if ( p =3D=3D 0.0 ) {=0A= return(Math.NEGATIVE_INFINITY);=0A= } else if ( p >=3D 1.0 ) {=0A= return(Math.POSITIVE_INFINITY);=0A= } else {=0A= return(Math.sqrt(2.0) * erfInv(2*p - 1));=0A= }=0A= }=0A= =0A= function erfInv(y) {=0A= var a =3D [ 0.886226899, -1.645349621, 0.914624893, -0.140543331];=0A= var b =3D [-2.118377725, 1.442710462, -0.329097515, 0.012229801];=0A= var c =3D [-1.970840454, -1.624906493, 3.429567803, 1.641345311];=0A= var d =3D [ 3.543889200, 1.637067800];=0A= var y0 =3D 0.7;=0A= var x =3D 0;=0A= var z =3D 0;=0A= if (Math.abs(y) <=3D y0) {=0A= z =3D y*y;=0A= x =3D y * (((a[3]*z+a[2])*z+a[1])*z+a[0])/=0A= ((((b[3]*z+b[2])*z+b[1])*z+b[0])*z+1.0);=0A= } else if (y > y0 && y < 1.0) {=0A= z =3D Math.sqrt(-Math.log((1-y)/2));=0A= x =3D (((c[3]*z+c[2])*z+c[1])*z+c[0]) / ((d[1]*z+d[0])*z+1);=0A= } else if (y < -y0 && y > -1) {=0A= z =3D Math.sqrt(-Math.log((1+y)/2));=0A= x =3D -(((c[3]*z+c[2])*z+c[1])*z+c[0])/ ((d[1]*z+d[0])*z+1);=0A= }=0A= x =3D x - (1.0 - erfc(x) - y) / (2/Math.sqrt(Math.PI) * = Math.exp(-x*x));=0A= x =3D x - (1.0 - erfc(x) - y) / (2/Math.sqrt(Math.PI) * = Math.exp(-x*x));=0A= =0A= return(x);=0A= } // ends erfInv=0A= =0A= function betaCdf( x, a, b) {=0A= if (a <=3D 0 || b <=3D 0) {=0A= return(Math.NaN);=0A= } else if (x >=3D 1) {=0A= return(1.0);=0A= } else if ( x > 0.0) {=0A= return(Math.min(incBeta(x ,a ,b),1.0));=0A= } else {=0A= return(0.0);=0A= }=0A= }=0A= =0A= function betaPdf( x, a, b) {=0A= if (a <=3D 0 || b <=3D 0 || x < 0 || x > 1) {=0A= return(Math.NaN);=0A= } else if ((x =3D=3D 0 && a < 1) || (x =3D=3D 2 && b < 1)) {=0A= return(Math.POSITIVE_INFINITY);=0A= } else if (!(a <=3D 0 || b <=3D 0 || x <=3D 0 || x >=3D 1)) {=0A= return(Math.exp((a - 1)*Math.log(x) + (b-1)*Math.log(1 - x) - = lnBeta(a,b)));=0A= } else {=0A= return(0.0);=0A= }=0A= }=0A= =0A= function lnBeta( x, y) {=0A= return(lnGamma(x) + lnGamma(y) - lnGamma(x+y));=0A= }=0A= =0A= function betaInv( p, a, b) {=0A= if (p < 0 || p > 1 || a <=3D 0 || b <=3D 0) {=0A= return(Math.NaN);=0A= } else if ( p =3D=3D 0 ) {=0A= return(Math.NEGATIVE_INFINITY);=0A= } else if ( p =3D=3D 1) {=0A= return(Math.POSITIVE_INFINITY);=0A= } else {=0A= var maxIt =3D 100;=0A= var it =3D 0;=0A= var tol =3D Math.sqrt(eps);=0A= var work =3D 1.0;=0A= var next;=0A= var x;=0A= if (a =3D=3D 0.0 ) {=0A= x =3D Math.sqrt(eps);=0A= } else if ( b =3D=3D 0.0) {=0A= x =3D 1 - Math.sqrt(eps);=0A= } else {=0A= x =3D a/(a+b);=0A= }=0A= while (Math.abs(work) > tol*Math.abs(x) && Math.abs(work) > tol = && it < maxIt) {=0A= it++;=0A= work =3D (betaCdf(x,a,b) - p)/betaPdf(x,a,b);=0A= next =3D x - work;=0A= while (next < 0 || next > 1) {=0A= work =3D work/2;=0A= next =3D x - work;=0A= }=0A= x =3D next;=0A= }=0A= return(x);=0A= }=0A= }=0A= =0A= function lnGamma(x) {=0A= /* natural ln(gamma(x)) without computing gamma(x)=0A= P.B. Stark, stark@stat.berkeley.edu=0A= =0A= JavaScript subroutine is based on a MATLAB program by C. Moler,=0A= in turn based on a FORTRAN program by W. J. Cody,=0A= Argonne National Laboratory, NETLIB/SPECFUN, June 16, 1988.=0A= =0A= References:=0A= =0A= 1) W. J. Cody and K. E. Hillstrom, 'Chebyshev Approximations for=0A= the Natural Logarithm of the Gamma Function,' Math. Comp. 21,=0A= 1967, pp. 198-203.=0A= =0A= 2) K. E. Hillstrom, ANL/AMD Program ANLC366S, DGAMMA/DLGAMA, May,=0A= 1969.=0A= =0A= 3) Hart, Et. Al., Computer Approximations, Wiley and sons, New=0A= York, 1968.=0A= */=0A= =0A= var d1 =3D -5.772156649015328605195174e-1;=0A= var p1 =3D [4.945235359296727046734888e0, = 2.018112620856775083915565e2,=0A= 2.290838373831346393026739e3, 1.131967205903380828685045e4,=0A= 2.855724635671635335736389e4, 3.848496228443793359990269e4,=0A= 2.637748787624195437963534e4, 7.225813979700288197698961e3];=0A= var q1 =3D [6.748212550303777196073036e1, = 1.113332393857199323513008e3,=0A= 7.738757056935398733233834e3, 2.763987074403340708898585e4,=0A= 5.499310206226157329794414e4, 6.161122180066002127833352e4,=0A= 3.635127591501940507276287e4, 8.785536302431013170870835e3];=0A= var d2 =3D 4.227843350984671393993777e-1;=0A= var p2 =3D [4.974607845568932035012064e0, = 5.424138599891070494101986e2,=0A= 1.550693864978364947665077e4, 1.847932904445632425417223e5,=0A= 1.088204769468828767498470e6, 3.338152967987029735917223e6,=0A= 5.106661678927352456275255e6, 3.074109054850539556250927e6];=0A= var q2 =3D [1.830328399370592604055942e2, = 7.765049321445005871323047e3,=0A= 1.331903827966074194402448e5, 1.136705821321969608938755e6,=0A= 5.267964117437946917577538e6, 1.346701454311101692290052e7,=0A= 1.782736530353274213975932e7, 9.533095591844353613395747e6];=0A= var d4 =3D 1.791759469228055000094023e0;=0A= var p4 =3D [1.474502166059939948905062e4, = 2.426813369486704502836312e6,=0A= 1.214755574045093227939592e8, 2.663432449630976949898078e9,=0A= 2.940378956634553899906876e10, 1.702665737765398868392998e11,=0A= 4.926125793377430887588120e11, 5.606251856223951465078242e11];=0A= var q4 =3D [2.690530175870899333379843e3, = 6.393885654300092398984238e5,=0A= 4.135599930241388052042842e7, 1.120872109616147941376570e9,=0A= 1.488613728678813811542398e10, 1.016803586272438228077304e11,=0A= 3.417476345507377132798597e11, 4.463158187419713286462081e11];=0A= var c =3D [-1.910444077728e-03, 8.4171387781295e-04,=0A= -5.952379913043012e-04, 7.93650793500350248e-04,=0A= -2.777777777777681622553e-03, 8.333333333333333331554247e-02,=0A= 5.7083835261e-03];=0A= =0A= var lng =3D Math.NaN;=0A= var mach =3D 1.e-12;=0A= var den =3D 1.0;=0A= var num =3D 0;=0A= var xm1, xm2, xm4;=0A= =0A= if (x < 0) {=0A= return(lng);=0A= } else if (x <=3D mach) {=0A= return(-Math.log(x));=0A= } else if (x <=3D 0.5) {=0A= for (var i =3D 0; i < 8; i++) {=0A= num =3D num * x + p1[i];=0A= den =3D den * x + q1[i];=0A= }=0A= lng =3D -Math.log(x) + (x * (d1 + x * (num/den)));=0A= } else if (x <=3D 0.6796875) {=0A= xm1 =3D x - 1.0;=0A= for (var i =3D 0; i < 8; i++) {=0A= num =3D num * xm1 + p2[i];=0A= den =3D den * xm1 + q2[i];=0A= }=0A= lng =3D -Math.log(x) + xm1 * (d2 + xm1*(num/den));=0A= } else if (x <=3D 1.5) {=0A= xm1 =3D x - 1.0;=0A= for (var i =3D 0; i < 8; i++) {=0A= num =3D num*xm1 + p1[i];=0A= den =3D den*xm1 + q1[i];=0A= }=0A= lng =3D xm1 * (d1 + xm1*(num/den));=0A= } else if (x <=3D 4.0) {=0A= xm2 =3D x - 2.0;=0A= for (var i =3D 0; i<8; i++) {=0A= num =3D num*xm2 + p2[i];=0A= den =3D den*xm2 + q2[i];=0A= }=0A= lng =3D xm2 * (d2 + xm2 * (num/den));=0A= } else if (x <=3D 12) {=0A= xm4 =3D x - 4.0;=0A= den =3D -1.0;=0A= for (var i =3D 0; i < 8; i++) {=0A= num =3D num * xm4 + p4[i];=0A= den =3D den * xm4 + q4[i];=0A= }=0A= lng =3D d4 + xm4 * (num/den);=0A= } else {=0A= var r =3D c[6];=0A= var xsq =3D x * x;=0A= for (var i =3D 0; i < 6; i++) {=0A= r =3D r / xsq + c[i];=0A= }=0A= r =3D r / x;=0A= var lnx =3D Math.log(x);=0A= var spi =3D 0.9189385332046727417803297;=0A= lng =3D r + spi - 0.5*lnx + x*(lnx-1);=0A= }=0A= return(lng);=0A= } // ends lnGamma=0A= =0A= =0A= function normPdf( mu, sigma, x) {=0A= return(Math.exp(-(x-mu)*(x-mu)/(2*sigma*sigma))/=0A= (Math.sqrt(2*Math.PI)*sigma));=0A= } // ends normPdf=0A= =0A= =0A= function tCdf(df, x) { // cdf of Student's t distribution with df = degrees of freedom=0A= var ans;=0A= if (df < 1) {=0A= ans =3D Math.NaN;=0A= } else if (x =3D=3D 0.0) {=0A= ans =3D 0.5;=0A= } else if (df =3D=3D 1) {=0A= ans =3D .5 + Math.atan(x)/Math.PI;=0A= } else if (x > 0) {=0A= ans =3D 1 - (incBeta(df/(df+x*x), df/2.0, 0.5))/2;=0A= } else if (x < 0) {=0A= ans =3D incBeta(df/(df+x*x), df/2.0, 0.5)/2;=0A= }=0A= return(ans);=0A= }=0A= =0A= function tInv(p, df ) { // inverse Student-t distribution with=0A= // df degrees of freedom=0A= var z;=0A= if (df < 0 || p < 0) {=0A= return(Math.NaN);=0A= } else if (p =3D=3D 0) {=0A= return(Math.NEGATIVE_INFINITY);=0A= } else if (p =3D=3D 1) {=0A= return(Math.POSITIVE_INFINITY);=0A= } else if (df =3D=3D 1) {=0A= return(Math.tan(Math.PI*(p-0.5)));=0A= } else if ( p >=3D 0.5) {=0A= z =3D betaInv(2.0*(1-p),df/2.0,0.5);=0A= return(Math.sqrt(df/z - df));=0A= } else {=0A= z =3D betaInv(2.0*p,df/2.0,0.5);=0A= return(-Math.sqrt(df/z - df));=0A= }=0A= }=0A= =0A= function incBeta(x, a, b) { // incomplete beta function=0A= // I_x(z,w) =3D 1/beta(z,w) * integral from 0 to x of t^(z-1) * = (1-t)^(w-1) dt=0A= // Ref: Abramowitz & Stegun, Handbook of Mathemtical Functions, = sec. 26.5.=0A= var res;=0A= if (x < 0 || x > 1) {=0A= res =3D Math.NaN;=0A= } else {=0A= res =3D 0;=0A= var bt =3D Math.exp(lnGamma(a+b) - lnGamma(a) - lnGamma(b) +=0A= a*Math.log(x) + b*Math.log(1-x));=0A= if (x < (a+1)/(a+b+2)) {=0A= res =3D bt * betaGuts(x, a, b) / a;=0A= } else {=0A= res =3D 1 - bt*betaGuts(1-x, b, a) / b;=0A= }=0A= }=0A= return(res);=0A= }=0A= =0A= function betaGuts( x, a, b) { // guts of the incomplete beta function=0A= var ap1 =3D a + 1;=0A= var am1 =3D a - 1;=0A= var apb =3D a + b;=0A= var am =3D 1;=0A= var bm =3D am;=0A= var y =3D am;=0A= var bz =3D 1 - apb*x/ap1;=0A= var d =3D 0;=0A= var app =3D d;=0A= var ap =3D d;=0A= var bpp =3D d;=0A= var bp =3D d;=0A= var yold =3D d;=0A= var m =3D 1;=0A= var t;=0A= while (y-yold > 4*eps*Math.abs(y)) {=0A= t =3D 2 * m;=0A= d =3D m * (b - m) * x / ((am1 + t) * (a + t));=0A= ap =3D y + d * am;=0A= bp =3D bz + d * bm;=0A= d =3D -(a + m) * (apb + m) * x / ((a + t) * (ap1 + t));=0A= app =3D ap + d * y;=0A= bpp =3D bp + d * bz;=0A= yold =3D y;=0A= am =3D ap / bpp;=0A= bm =3D bp / bpp;=0A= y =3D app / bpp;=0A= if (m =3D=3D 1) bz =3D 1;=0A= m++;=0A= }=0A= return(y);=0A= }=0A= =0A= function chi2Cdf( x, df ) {=0A= return(gammaCdf(x,df/2,2));=0A= }=0A= =0A= function chi2Inv( p, df ) { // kluge for chi-square quantile function.=0A= var guess =3D Math.NaN;=0A= if (p =3D=3D 0.0) {=0A= guess =3D 0.0;=0A= } else if ( p =3D=3D 1.0 ) {=0A= guess =3D Math.POSITIVE_INFINITY;=0A= } else if ( p < 0.0 ) {=0A= guess =3D Math.NaN;=0A= } else {=0A= var tolAbs =3D 1.0e-8;=0A= var tolRel =3D 1.0e-3;=0A= guess =3D Math.max(0.0, df + Math.sqrt(2*df)*normInv(p)); // = guess from normal approx =0A= var currP =3D chi2Cdf( guess, df);=0A= var loP =3D currP;=0A= var hiP =3D currP;=0A= var guessLo =3D guess;=0A= var guessHi =3D guess;=0A= while (loP > p) { // step down=0A= guessLo =3D 0.8*guessLo;=0A= loP =3D chi2Cdf( guessLo, df);=0A= }=0A= while (hiP < p) { // step up=0A= guessHi =3D 1.2*guessHi;=0A= hiP =3D chi2Cdf( guessHi, df);=0A= }=0A= guess =3D (guessLo + guessHi)/2.0;=0A= currP =3D chi2Cdf( guess, df);=0A= while ( (Math.abs(currP - p) > tolAbs) || (Math.abs(currP - p)/p = > tolRel) ) { // bisect=0A= if ( currP < p ) {=0A= guessLo =3D guess;=0A= } else {=0A= guessHi =3D guess;=0A= } =0A= guess =3D (guessLo + guessHi)/2.0;=0A= currP =3D chi2Cdf(guess, df);=0A= }=0A= }=0A= return(guess);=0A= }=0A= =0A= function gammaCdf( x, a, b) { // gamma distribution CDF.=0A= var p =3D Math.NaN;=0A= if (a <=3D 0 || b <=3D 0) {=0A= } else if (x <=3D 0) {=0A= p =3D 0.0;=0A= } else {=0A= p =3D Math.min(incGamma(x/b, a), 1.0);=0A= }=0A= return(p);=0A= }=0A= =0A= function incGamma( x, a) {=0A= var inc =3D 0;=0A= var gam =3D lnGamma(a+rmin);=0A= if (x =3D=3D 0) {=0A= inc =3D 0;=0A= } else if (a =3D=3D 0) {=0A= inc =3D 1;=0A= } else if (x < a+1) {=0A= var ap =3D a;=0A= var sum =3D 1.0/ap;=0A= var del =3D sum;=0A= while (Math.abs(del) >=3D 10*eps*Math.abs(sum)) {=0A= del *=3D x/(++ap);=0A= sum +=3D del;=0A= }=0A= inc =3D sum * Math.exp(-x + a*Math.log(x) - gam);=0A= } else if (x >=3D a+1) {=0A= var a0 =3D 1;=0A= var a1 =3D x;=0A= var b0 =3D 0;=0A= var b1 =3D 1;=0A= var fac =3D 1;=0A= var n =3D 1;=0A= var g =3D 1;=0A= var gold =3D 0;=0A= var ana;=0A= var anf;=0A= while (Math.abs(g-gold) >=3D 10*eps*Math.abs(g)) {=0A= gold =3D g;=0A= ana =3D n - a;=0A= a0 =3D (a1 + a0 *ana) * fac;=0A= b0 =3D (b1 + b0 *ana) * fac;=0A= anf =3D n*fac;=0A= a1 =3D x * a0 + anf * a1;=0A= b1 =3D x * b0 + anf * b1;=0A= fac =3D 1.0 / a1;=0A= g =3D b1 * fac;=0A= n++;=0A= }=0A= inc =3D 1 - Math.exp(-x + a*Math.log(x) - gam) * g;=0A= }=0A= return(inc);=0A= }=0A= =0A= function poissonPmf( lambda, k) {=0A= var p =3D 0.0;=0A= if (k >=3D 0) {=0A= p =3D Math.exp(-lambda)*Math.pow(lambda,k)/factorial(k);=0A= }=0A= return(p);=0A= }=0A= =0A= function poissonCdf( lambda, k) {=0A= var p =3D 0;=0A= var b =3D 0;=0A= var m =3D 0;=0A= while (m <=3D k) {=0A= b +=3D Math.pow(lambda, m++)/factorial(k);=0A= }=0A= p +=3D Math.exp(-lambda)*b;=0A= return(p);=0A= }=0A= =0A= function poissonTail(lambda, k) {=0A= return(1.0-poissonCdf(lambda, k-1));=0A= }=0A= =0A= =0A= function factorial(n) { // computes n!=0A= var fac=3D1;=0A= for (var i=3Dn; i > 1; i--) {fac *=3D i;}=0A= return(fac);=0A= }=0A= =0A= function binomialCoef(n,k) { // computes n choose k=0A= if (n < k || n < 0) {=0A= return(0.0);=0A= } else if ( k =3D=3D 0 || n =3D=3D 0 || n =3D=3D k) {=0A= return(1.0);=0A= } else {=0A= var minnk =3D Math.min(k, n-k);=0A= var coef =3D 1;=0A= for (var j =3D 0; j < minnk; j++) {=0A= coef *=3D (n-j)/(minnk-j);=0A= }=0A= return(coef);=0A= }=0A= }=0A= =0A= function binomialPmf(n, p, k) { // binomial pmf at k.=0A= var pmf =3D binomialCoef(n,k)*Math.pow(p,k)*Math.pow((1-p),(n-k));=0A= return(pmf);=0A= }=0A= =0A= function binomialCdf(n, p, k) { // binomial CDF: Pr(X <=3D k), X~B(n,p)=0A= if (k < 0) {=0A= return(0.0);=0A= } else if (k >=3D n) {=0A= return(1.0);=0A= } else {=0A= var cdf =3D 0.0;=0A= for (var i =3D 0; i <=3D k; i++) {=0A= cdf +=3D binomialPmf(n, p, i);=0A= }=0A= return(cdf);=0A= }=0A= }=0A= =0A= function binomialTail(n,p,k) { // binomial tail probability Pr(X >=3D = k), X~B(n,p)=0A= if (k < 0) {=0A= return(1.0);=0A= } else if (k >=3D n) {=0A= return(0.0);=0A= } else {=0A= var tailP =3D 0.0;=0A= for (var i =3D k; i <=3D n; i++) {=0A= tailP +=3D binomialPmf(n, p, i);=0A= }=0A= return(tailP);=0A= }=0A= }=0A= =0A= function binomialInv(n, p, pt) { // binomial percentile function=0A= var t =3D 0;=0A= if (pt < 0 || pt > 1) {=0A= t =3D NaN;=0A= } else if (pt =3D=3D 0.0) {=0A= t =3D 0;=0A= } else if (pt =3D=3D 1.0) {=0A= t =3D n;=0A= } else {=0A= var t =3D 0;=0A= var pc =3D 0.0;=0A= while ( pc < pt ) {=0A= pc +=3D binomialPmf(n, p, t++);=0A= }=0A= t -=3D 1;=0A= }=0A= return(t);=0A= }=0A= =0A= function multinomialCoef(list, n) { // multinomial coefficient.=0A= // WARNING: not very stable algorithm; avoid for large n.=0A= var val =3D 0; =0A= var lmn =3D vMinMax(list);=0A= if (typeof(n) =3D=3D 'undefined' || n =3D=3D null) {=0A= n =3D vSum(list);=0A= }=0A= if (lmn[0] < 0.0) {=0A= alert('Error #1 in irGrade.multinomialCoef: a number of outcomes = is negative!');=0A= } else if (n =3D=3D vSum(list)) {=0A= val =3D factorial(n);=0A= for (var i=3D0; i < list.length; i++) {=0A= val /=3D factorial(list[i]);=0A= }=0A= }=0A= return(val); =0A= }=0A= =0A= function multinomialPmf(olist, plist, n) { // multinomial pmf; not = stable algorithm=0A= var val =3D 0.0;=0A= var pmn =3D vMinMax(plist);=0A= var omn =3D vMinMax(olist);=0A= if (typeof(n) =3D=3D 'undefined' || n =3D=3D null) {=0A= n =3D vSum(olist);=0A= }=0A= if (olist.length !=3D plist.length) {=0A= alert('Error #1 in irGrade.multinomialPmf: length of outcome and = probability vectors ' +=0A= 'do not match!');=0A= } else if (pmn[0] < 0.0) {=0A= alert('Error #2 in irGrade.multinomialPmf: a probability is = negative!');=0A= } else if (omn[0] < 0.0) {=0A= alert('Error #3 in irGrade.multinomialPmf: a number of outcomes = is negative!');=0A= } else if (n =3D=3D vSum(olist)) {=0A= var pl =3D vMult(1.0/vSum(plist), plist); // just in case=0A= val =3D factorial(n);=0A= for (var i=3D0; i< olist.length; i++) {=0A= val *=3D Math.pow(pl[i], olist[i])/factorial(olist[i]);=0A= }=0A= }=0A= return(val);=0A= }=0A= =0A= =0A= function geoPmf( p, k) {=0A= // chance it takes k trials to the first success in iid Bernoulli(p) = trials=0A= // EX =3D 1/p; SD(X) =3D sqrt(1-p)/p=0A= if (k < 1 || p =3D=3D 0.0) {=0A= return(0.0);=0A= } else {=0A= return(Math.pow((1-p),k-1)*p);=0A= }=0A= }=0A= =0A= function geoCdf( p, k) {=0A= // chance it takes k or fewer trials to the first success in iid = Bernoulli(p) trials=0A= if (k < 1 || p =3D=3D 0.0) {=0A= return(0.0);=0A= } else {=0A= return(1-Math.pow( 1-p, k));=0A= }=0A= }=0A= =0A= function geoTail( p, k) {=0A= // chance of k or more trials to the first success in iid Bernoulli(p) = trials=0A= return(1 - geoCdf(p, k-1));=0A= }=0A= =0A= function geoInv(p, pt) { // geometric percentile function=0A= var t =3D 0;=0A= if (pt < 0 || pt > 1) {=0A= t =3D Math.NaN;=0A= } else if (pt =3D=3D 0.0) {=0A= t =3D 0;=0A= } else if (pt =3D=3D 1.0) {=0A= t =3D Math.POSITIVE_INFINITY;=0A= } else {=0A= var t =3D 0;=0A= var pc =3D 0.0;=0A= while ( pc < pt ) {=0A= pc +=3D geoPmf(p, t++);=0A= }=0A= }=0A= return(t);=0A= }=0A= =0A= function hyperGeoPmf( N, M, n, m) {=0A= // chance of drawing m of M objects in a sample of size n from=0A= // N objects in all. p =3D (M C m)*(N-M C n-m)/(N C n)=0A= // EX =3D n*M/N; SD(X)=3D sqrt((N-n)/(N-1))*sqrt(np(1-p));=0A= var p;=0A= if ( n < m || N < M || M < m || m < 0 || N < 0) {=0A= return(0.0);=0A= } else {=0A= p =3D binomialCoef(M,m)*binomialCoef(N-M,n-m)/binomialCoef(N,n);=0A= return(p);=0A= }=0A= }=0A= =0A= function hyperGeoCdf( N, M, n, m) {=0A= // chance of drawing m or fewer of M objects in a sample of size n from=0A= // N objects in all=0A= var p=3D0.0;=0A= var mMax =3D Math.min(m,M);=0A= mMax =3D Math.min(mMax,n);=0A= for (var i =3D 0; i <=3D mMax; i++) {=0A= p +=3D hyperGeoPmf(N, M, n, i);=0A= }=0A= return(p);=0A= }=0A= =0A= function hyperGeoTail( N, M, n, m) {=0A= // chance of drawing m or more of M objects in a sample of size n from=0A= // N objects in all=0A= var p=3D0.0;=0A= for (var i =3D m; i <=3D M; i++) {=0A= p +=3D hyperGeoPmf(N, M, n, i);=0A= }=0A= return(p);=0A= }=0A= =0A= function negBinomialPmf( p, s, t) {=0A= // chance that the sth success in iid Bernoulli trials is on the tth = trial=0A= // EX =3D s/p; SD(X) =3D sqrt(s(1-p))/p=0A= if (s > t || s < 0) {=0A= return(0.0);=0A= }=0A= var prob =3D p*binomialPmf(t-1,p,s-1);=0A= return(prob);=0A= }=0A= =0A= function negBinomialCdf( p, s, t) {=0A= // chance the sth success in iid Bernoulli trials is on or before the = tth trial=0A= var prob =3D 0.0;=0A= for (var i =3D s; i <=3D t; i++) {=0A= prob +=3D negBinomialPmf(p, s, i);=0A= }=0A= return(prob);=0A= }=0A= =0A= function pDieRolls(rolls,spots) { // chance that the sum of 'rolls' = rolls of a die =3D 'spots'=0A= if (rolls > 4) {=0A= alert("Error #1 in irGrade.pDiceRolls: too many rolls " + rolls = + ". ");=0A= return(Math.NaN);=0A= } else { // BRUTE FORCE!=0A= var found =3D 0;=0A= if (spots < rolls || spots > 6*rolls) {return(0.0);}=0A= var possible =3D Math.pow(6,rolls);=0A= if (rolls =3D=3D 1) {=0A= return(1/possible);=0A= } else if (rolls =3D=3D 2) {=0A= for (var i=3D1; i <=3D6; i++ ) {=0A= for (var j=3D1; j <=3D 6; j++ ) {=0A= if (i+j =3D=3D spots ) {found++;}=0A= }=0A= }=0A= } else if (rolls =3D=3D 3 ) {=0A= for (var i=3D1; i <=3D6; i++ ) {=0A= for (var j=3D1; j<=3D6; j++ ) {=0A= for (var k=3D1; k<=3D6; k++ ) {=0A= if (i+j+k =3D=3D spots ) {found++;}=0A= }=0A= }=0A= }=0A= } else if (rolls =3D=3D 4 ) {=0A= for (var i=3D1; i <=3D6; i++ ) {=0A= for (var j=3D1; j<=3D6; j++ ) {=0A= for (var k=3D1; k<=3D6; k++ ) {=0A= for (var m=3D1; m <=3D6; m++ ) {=0A= if (i+j+k+m =3D=3D spots ) {found++;}=0A= }=0A= }=0A= }=0A= }=0A= }=0A= return(found/possible);=0A= }=0A= return(false);=0A= }=0A= =0A= function permutations(n,k) { // number of permutations of k of n things=0A= if (n < k || n < 0) {=0A= return(0);=0A= } else if ( k=3D=3D0 || n =3D=3D 0) {=0A= return(1);=0A= } else {=0A= var coef=3D1;=0A= for (var j=3D0; j < k; j++) coef *=3D (n-j);=0A= }=0A= return(coef);=0A= }=0A= =0A= =0A= function sgn(x) { // signum function=0A= if (x >=3D 0) {=0A= return(1);=0A= } else if (x < 0) {=0A= return (-1);=0A= }=0A= }=0A= =0A= function linspace(lo,hi,n) { // n linearly spaced points between lo and = hi=0A= var spaced =3D new Array(n);=0A= var dx =3D(hi-lo)/(n-1);=0A= for (var i=3D0; i < n; i++) {=0A= spaced[i] =3D lo + i*dx;=0A= }=0A= return(spaced);=0A= }=0A= =0A= function rms(list) { // rms=0A= var r =3D 0;=0A= for (var i=3D0; i < list.length; i++) r +=3D list[i]*list[i];=0A= r /=3D list.length;=0A= return(Math.sqrt(r));=0A= }=0A= =0A= function vMinMax(list){ // returns min and max of list=0A= var mn =3D list[0];=0A= var mx =3D list[0];=0A= for (var i=3D1; i < list.length; i++) {=0A= if (mn > list[i]) mn =3D list[i];=0A= if (mx < list[i]) mx =3D list[i];=0A= }=0A= var vmnmx =3D new Array(mn,mx);=0A= return(vmnmx);=0A= }=0A= =0A= function vMinMaxIndices(list){ // returns min, max, index of min, index = of max=0A= var mn =3D list[0];=0A= var indMn =3D 0;=0A= var mx =3D list[0];=0A= var indMx =3D 0;=0A= for (var i=3D1; i < list.length; i++) {=0A= if (mn > list[i]) {=0A= mn =3D list[i];=0A= indMn =3D i;=0A= }=0A= if (mx < list[i]) {=0A= mx =3D list[i];=0A= indMx =3D i;=0A= }=0A= }=0A= var vmnmx =3D new Array(mn,mx,indMn,indMx);=0A= return(vmnmx);=0A= }=0A= =0A= function vMinMaxAbs(list) {=0A= // returns min and max of absolute values of a list's elements=0A= var mn =3D Math.abs(list[0]);=0A= var mx =3D Math.abs(list[0]);=0A= var val;=0A= for (var i=3D1; i < list.length; i++) {=0A= val =3D Math.abs(list[i]);=0A= if (mn > val) mn =3D val;=0A= if (mx < val) mx =3D val;=0A= }=0A= var vmnmx =3D new Array(mn,mx);=0A= return(vmnmx);=0A= }=0A= =0A= function randBoolean(p){ // random boolean value, prob p that it is true=0A= if (typeof(p) =3D=3D 'undefined' || p =3D=3D null) {=0A= p =3D 0.5;=0A= }=0A= if (rand.next() <=3D p) {=0A= return(false);=0A= } else {=0A= return(true);=0A= }=0A= }=0A= =0A= function sortUnique(list,order) { // sort a list, remove duplicate = entries=0A= var temp =3D list;=0A= if (typeof(order) !=3D 'undefined' && order !=3D null) {=0A= temp.sort(order);=0A= } else {=0A= temp.sort();=0A= }=0A= var temp2 =3D new Array(temp.length);=0A= temp2[0] =3D temp[0];=0A= var ix =3D 0;=0A= for (var i=3D1; i < temp.length; i++) {=0A= if (temp[i] !=3D temp2[ix] ) {=0A= temp2[++ix] =3D temp[i];=0A= }=0A= }=0A= return(temp2);=0A= }=0A= =0A= function randPermutation(list,index) { // returns a random permutation = of list=0A= var randIndex =3D = listOfDistinctRandInts(list.length,0,list.length-1);=0A= var thePermutation =3D new Array(list.length);=0A= for (var i=3D0; i < list.length; i++) {=0A= thePermutation[i] =3D list[randIndex[i]];=0A= }=0A= if (typeof(index) !=3D 'undefined' && index =3D=3D 'forward') { // = original indices=0A= var p =3D new Array(2);=0A= p[0] =3D thePermutation;=0A= p[1] =3D randIndex;=0A= thePermutation =3D p;=0A= } else if (typeof(index) !=3D 'undefined' && index =3D=3D 'inverse') = { // inverse permutation=0A= var p =3D new Array(2);=0A= p[0] =3D thePermutation;=0A= p[1] =3D new Array(list.length);=0A= for (var i=3D0; i < list.length; i++) {=0A= p[1][randIndex[i]] =3D i;=0A= }=0A= thePermutation =3D p;=0A= }=0A= return(thePermutation);=0A= }=0A= =0A= function fakeBivariateData(nPoints, funArray, heteroFac, snr, loEnd, = hiEnd) {=0A= // returns a 2-d array of synthetic data generated from a polynomial,=0A= // according to the contents of funArray.=0A= // if funArray[0] =3D=3D "polynomial", uses the other elements of = funArray as=0A= // the coefficients of a polynomial.=0A= // funArray[1] + funArray[2]*X + funArray[3]*X^2 + ...=0A= // 1/3 of the points have noise level heteroFac times larger than the = rest.=0A= // Normalizes the errors to signal/noise ratio snr in 2-norm=0A= var data =3D new Array(2);=0A= data[0] =3D new Array(nPoints);=0A= data[1] =3D new Array(nPoints);=0A= var x;=0A= var fVal;=0A= var xPow;=0A= if (funArray[0] =3D=3D "polynomial") {=0A= if (typeof(loEnd) =3D=3D 'undefined' || loEnd =3D=3D null) { = // lower limit of X variable=0A= loEnd =3D -10;=0A= }=0A= if (typeof(hiEnd) =3D=3D 'undefined' || hiEnd =3D=3D null) { = // upper limit of X variable=0A= hiEnd =3D 10;=0A= }=0A= var dX =3D (hiEnd - loEnd)/(nPoints - 1);=0A= for (var i=3D0; i < nPoints; i++) {=0A= x =3D loEnd + i*dX;=0A= data[0][i] =3D x;=0A= fVal =3D 0.0;=0A= xPow =3D 1.0;=0A= for (var j=3D1; j < funArray.length; j++) {=0A= fVal +=3D xPow*funArray[j];=0A= xPow *=3D x;=0A= }=0A= data[1][i] =3D fVal;=0A= }=0A= } else {=0A= alert('Error #1 in irGrade.fakeBivariateData()!\n' +=0A= 'Unsupported function type: ' + funArray[0].toString());=0A= return(null);=0A= }=0A= // now add noise.=0A= var sigNorm =3D twoNorm(data[1]);=0A= var noise =3D new Array(nPoints);=0A= for (var i=3D0; i < nPoints; i++) {=0A= noise[i] =3D rNorm();=0A= }=0A= // pick a random set to perturb for heteroscedastic noise=0A= var segLen =3D Math.floor(nPoints/3);=0A= var startPt =3D Math.floor(2*nPoints/3*rand.next());=0A= for (var i=3DstartPt; i < startPt+segLen; i++) {=0A= noise[i] =3D noise[i]*heteroFac;=0A= }=0A= var noiseNorm =3D twoNorm(noise);=0A= for (var i=3D0; i < nPoints; i++) {=0A= data[1][i] +=3D noise[i]*sigNorm/noiseNorm/snr;=0A= }=0A= return(data)=0A= }=0A= =0A= function nextRand() { // generates next random number in a sequence=0A= var up =3D this.seed / this.Q;=0A= var lo =3D this.seed % this.Q;=0A= var trial =3D this.A * lo - this.R * up;=0A= if (trial > 0) {=0A= this.seed =3D trial;=0A= } else {=0A= this.seed =3D trial + this.M;=0A= }=0A= return (this.seed * this.oneOverM);=0A= }=0A= =0A= function rng(s) {=0A= if ( typeof(s)=3D=3D'undefined' || s =3D=3D null ){=0A= var d =3D new Date();=0A= this.seed =3D 2345678901=0A= + (d.getSeconds() * 0xFFFFFF)=0A= + (d.getMinutes() * 0xFFFF);=0A= } else {=0A= this.seed =3D s;=0A= }=0A= this.A =3D 48271;=0A= this.M =3D 2147483647;=0A= this.Q =3D this.M / this.A;=0A= this.R =3D this.M % this.A;=0A= this.oneOverM =3D 1.0 / this.M;=0A= this.next =3D nextRand;=0A= this.getSeed =3D getRandSeed;=0A= return(this);=0A= }=0A= =0A= function getRandSeed() { // get seed of random number generator=0A= return(this.seed);=0A= }=0A= =0A= function crypt(s,t) {=0A= var slen =3D s.length;=0A= var tlen =3D t.length;=0A= var rad =3D 16;=0A= var r =3D 0;=0A= var i;=0A= var j =3D -1;=0A= var result =3D '';=0A= if (s.substr(0,2) =3D=3D "0x") {=0A= for (i=3D2; i < slen; i+=3D2) {=0A= if (++j >=3D tlen) {j =3D 0;}=0A= r =3D parseInt(s.substr(i,2),rad) ^ t.charCodeAt(j);=0A= result +=3D String.fromCharCode(r);=0A= }=0A= } else {=0A= result +=3D'0x';=0A= for ( i=3D0; i < slen; i++) {=0A= if (++j >=3D tlen) {j =3D 0;}=0A= r =3D s.charCodeAt(i) ^ t.charCodeAt(j);=0A= result +=3D (r < rad ? "0" : "") + r.toString(rad);=0A= }=0A= }=0A= return(result);=0A= }=0A= ------=_NextPart_000_0000_01C283FA.710A0560--