<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>35.2.3.1 Discrete and continuous random variables</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p> Consider the following experiments. In each case state the sample space.</p>
<ol class="HELM_parts">
<li> The number, \(n\), of defective items in a batch of \({@itms@}\) is noted. </li>
<li> The weight, \(w\), in kg, of lubricating oil drained from a machine is determined using a spring
balance. Assume that there is at least some oil drained from the machine.</li>
<li> The natural logarithm of the weight, \(\ln{w}\), in kg, according to a spring balance, of lubricating
oil drained from a machine, is noted. Assume that there is at least some oil drained from the machine.</li>
</ol>
<p> In STACK connected intervals on the real line are typed the following way:</p>
<ul>
<li> \(\texttt{oo(a,b)}\) for the "open-open" interval \((a,b)\).</li>
<li> \(\texttt{oc(a,b)}\) for the "open-closed" interval \((a,b]\).</li>
<li> \(\texttt{co(a,b)}\) for the "closed-open" interval \([a,b)\).</li>
<li> \(\texttt{cc(a,b)}\) for the "closed-closed" interval \([a,b]\).</li>
</ul>
<p> The discrete set should be typed as \(\texttt{{a,b,c,d,...}}\). If you need to use \(\infty\), then type \(\texttt{inf}\) (type \(\texttt{-inf}\) for \(-\infty\)).</p>
<br>
<ol class="HELM_parts">
<li> The random variable \(n\) is discrete and is an element of the set [[input:ans1]][[validation:ans1]][[feedback:prt1]] </li>
<li> The random variable \(w\) is continuous and is an element of the set [[input:ans2]][[validation:ans2]][[feedback:prt2]] </li>
<li> The random variable \(\ln{w}\) is continuous and is an element of the set [[input:ans3]][[validation:ans3]][[feedback:prt3]] </li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li> \(n\in{@ta1@}\).</li>
    <li> \(w\in{@ta2@}\).</li>
    <li> \(\ln{w}\in{@ta3@}\).</li>
</ol>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2024072400</text>
    </stackversion>
    <questionvariables>
      <text>itms: 15 + rand(11);

/* Decided not to get them to determine whether the set is discrete or cts. Could do this as a preceding question? */
/* Helm workbooks gave this as {1,2,...} but it should include 0 (no defective items) */
ta1: setify(makelist(i,i,0,itms));
ta2: oo(0,inf);
ta3: oo(-inf,inf);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>Discrete set: \( {@ta1@} \)</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: green; --darkreader-inline-color:#72ff72;" data-darkreader-inline-color=""><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: orange; --darkreader-inline-color:#ffae1a;" data-darkreader-inline-color=""><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color: red; --darkreader-inline-color:#ff1a1a;" data-darkreader-inline-color=""><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>40</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>ta2</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <input>
      <name>ans3</name>
      <type>algebraic</type>
      <tans>ta3</tans>
      <boxsize>10</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
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      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
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      <forbidfloat>1</forbidfloat>
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      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>3</showvalidation>
      <options/>
    </input>
    <prt>
      <name>prt1</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
      </feedbackvariables>
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    </prt>
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      <value>1.0000000</value>
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      <feedbackstyle>1</feedbackstyle>
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        <answertest>AlgEquiv</answertest>
        <sans>ans2</sans>
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        <truescoremode>=</truescoremode>
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      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
      <feedbackstyle>1</feedbackstyle>
      <feedbackvariables>
        <text/>
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      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans3</sans>
        <tans>ta3</tans>
        <testoptions/>
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        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
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        <falseanswernote>prt3-1-F</falseanswernote>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>ta3</value>
      </testinput>
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        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
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      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt3-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>{1,2,3,4,5,6,7,8,9,10}</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>1</value>
      </testinput>
      <testinput>
        <name>ans3</name>
        <value>20</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt2-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt3</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
