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<h2 class="hd hd-2 unit-title">Problem set 3</h2>
<div class="vert-mod">
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<h2 class="hd hd-2 unit-title">Pset 3 problem checker</h2>
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Problem 1
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps3-1-check-problem-progress"></div>
<div class="problem">
<div>
<p>
To check your answers put them in the appropriate box and click the &#8216;Check' button. The checker can do arithmetic. So, 3^2, [mathjaxinline]5/3[/mathjaxinline] and [mathjaxinline]3*4[/mathjaxinline] are okay. </p>
<p>
Unless otherwise stated the checker expects numerical answers to 3 significant digits. </p>
<p>
For formulas you can use R notation. Remember to use a * for multiplication, i.e. [mathjaxinline]3*x[/mathjaxinline] <b class="bf">NOT </b> [mathjaxinline]3x[/mathjaxinline]. </p>
<p>
The checker knows many of the standard functions, e.g. use exp(x) and ln(x) for the exponential and natural log functions. </p>
<p>
The formula checker expects a specific letter for the variables, so be sure to use the ones specified. </p>
<p>
<b class="bf">1(a)</b>
<em>No answer checker given.</em>
</p>
<p>
<b class="bf">1(b)</b>
<em>No answer checker given.</em>
</p>
<p><b class="bf">1(c)</b> The problem asks for the values of [mathjaxinline]n[/mathjaxinline] that make the events independent. We'll give you the hint that [mathjaxinline]n=1[/mathjaxinline] is one value &#8211; you still need to explain this in your solutions. Give the other value.<br/><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-1-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
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<p id="answer_ps3-1-check_2_1" class="answer"/>
<div id="display_ps3-1-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-1-check_2_1_dynamath" name="input_ps3-1-check_2_1_dynamath"/>
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</div></div> </p>
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<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
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Problem 2
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps3-2-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">2(a)</b> Give the values to 3 significant digits </p>
<p>
Mean: <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-2-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-2-check_2_1" id="input_ps3-2-check_2_1" aria-describedby="status_ps3-2-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-2-check_2_1"/>
<span class="status unanswered" id="status_ps3-2-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<p id="answer_ps3-2-check_2_1" class="answer"/>
<div id="display_ps3-2-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-2-check_2_1_dynamath" name="input_ps3-2-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
Variance: <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps3-2-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-2-check_3_1" id="input_ps3-2-check_3_1" aria-describedby="status_ps3-2-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-2-check_3_1"/>
<span class="status unanswered" id="status_ps3-2-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-2-check_3_1" class="answer"/>
<div id="display_ps3-2-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-2-check_3_1_dynamath" name="input_ps3-2-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p>
Standard deviation: <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps3-2-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-2-check_4_1" id="input_ps3-2-check_4_1" aria-describedby="status_ps3-2-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-2-check_4_1"/>
<span class="status unanswered" id="status_ps3-2-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-2-check_4_1" class="answer"/>
<div id="display_ps3-2-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-2-check_4_1_dynamath" name="input_ps3-2-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p>
<b class="bf">2(b)</b>
<em>No answer checker given.</em>
</p>
<p>
<b class="bf">2(c)</b>
<em>No answer checker given.</em>
</p>
<p>
<b class="bf">2(d)</b>
<em>No answer checker given.</em>
</p>
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Problem 3
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps3-3-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">3(a)</b> Give the standard deviations to 3 significant digits. </p>
<p>
[mathjaxinline]\sigma _ X[/mathjaxinline]: <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-3-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-3-check_2_1" id="input_ps3-3-check_2_1" aria-describedby="status_ps3-3-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-3-check_2_1"/>
<span class="status unanswered" id="status_ps3-3-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-3-check_2_1" class="answer"/>
<div id="display_ps3-3-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-3-check_2_1_dynamath" name="input_ps3-3-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]\sigma _ Y[/mathjaxinline]: <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps3-3-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-3-check_3_1" id="input_ps3-3-check_3_1" aria-describedby="status_ps3-3-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-3-check_3_1"/>
<span class="status unanswered" id="status_ps3-3-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-3-check_3_1" class="answer"/>
<div id="display_ps3-3-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-3-check_3_1_dynamath" name="input_ps3-3-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]\sigma _ Z[/mathjaxinline]: <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps3-3-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-3-check_4_1" id="input_ps3-3-check_4_1" aria-describedby="status_ps3-3-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-3-check_4_1"/>
<span class="status unanswered" id="status_ps3-3-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-3-check_4_1" class="answer"/>
<div id="display_ps3-3-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-3-check_4_1_dynamath" name="input_ps3-3-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p>
<b class="bf">3(b)</b>
<em>No answer checker given.</em>
</p>
<p><b class="bf">3(c)</b> Expected <em>total</em> gain over 60 games:<br/><div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps3-3-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
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<input type="text" name="input_ps3-3-check_5_1" id="input_ps3-3-check_5_1" aria-describedby="status_ps3-3-check_5_1" value="" class="math" size="50"/>
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<div id="display_ps3-3-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-3-check_5_1_dynamath" name="input_ps3-3-check_5_1_dynamath"/>
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Problem 4
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<div class="problem">
<div>
<p><b class="bf">4(a)</b> Give the number of raisins in the box:<br/><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-4-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-4-check_2_1" id="input_ps3-4-check_2_1" aria-describedby="status_ps3-4-check_2_1" value="" class="math" size="50"/>
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<span class="status unanswered" id="status_ps3-4-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
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<div id="display_ps3-4-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-4-check_2_1_dynamath" name="input_ps3-4-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">4(b)</b> Give the formula for the pdf of [mathjaxinline]H[/mathjaxinline]. (Use the variable <tt class="tt">h.</tt>) </p>
<p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps3-4-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-4-check_3_1" id="input_ps3-4-check_3_1" aria-describedby="status_ps3-4-check_3_1" value="" class="math" size="60"/>
<span class="trailing_text" id="trailing_text_ps3-4-check_3_1"/>
<span class="status unanswered" id="status_ps3-4-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
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<div id="display_ps3-4-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-4-check_3_1_dynamath" name="input_ps3-4-check_3_1_dynamath"/>
</div>
</div></div>
</p>
<p><b class="bf">4(c)</b> Give the formula for the cdf of [mathjaxinline]H[/mathjaxinline]. (Use the variable <tt class="tt">h.</tt>) </p>
<p>
<div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps3-4-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-4-check_4_1" id="input_ps3-4-check_4_1" aria-describedby="status_ps3-4-check_4_1" value="" class="math" size="60"/>
<span class="trailing_text" id="trailing_text_ps3-4-check_4_1"/>
<span class="status unanswered" id="status_ps3-4-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
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<div id="display_ps3-4-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-4-check_4_1_dynamath" name="input_ps3-4-check_4_1_dynamath"/>
</div>
</div></div>
</p>
<p><b class="bf">4(d)</b> Probability a raisin is in the bottom third (3 significant digits):<br/><div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps3-4-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-4-check_5_1" id="input_ps3-4-check_5_1" aria-describedby="status_ps3-4-check_5_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-4-check_5_1"/>
<span class="status unanswered" id="status_ps3-4-check_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-4-check_5_1" class="answer"/>
<div id="display_ps3-4-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-4-check_5_1_dynamath" name="input_ps3-4-check_5_1_dynamath"/>
</div>
</div></div> </p>
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Problem 5
</h3>
<div class="problem-progress" id="block-v1:MITx+18.05r_10+2022_Summer+type@problem+block@ps3-5-check-problem-progress"></div>
<div class="problem">
<div>
<p><b class="bf">5(a)</b> Give the probabilities to 3 significant digits. </p>
<p>
[mathjaxinline]P(Z \le 0) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-5-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_2_1" id="input_ps3-5-check_2_1" aria-describedby="status_ps3-5-check_2_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_2_1"/>
<span class="status unanswered" id="status_ps3-5-check_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_2_1" class="answer"/>
<div id="display_ps3-5-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_2_1_dynamath" name="input_ps3-5-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]P(Z &gt; 1.5) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps3-5-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_3_1" id="input_ps3-5-check_3_1" aria-describedby="status_ps3-5-check_3_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_3_1"/>
<span class="status unanswered" id="status_ps3-5-check_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_3_1" class="answer"/>
<div id="display_ps3-5-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_3_1_dynamath" name="input_ps3-5-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]P(|Z| \le 1.5) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps3-5-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_4_1" id="input_ps3-5-check_4_1" aria-describedby="status_ps3-5-check_4_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_4_1"/>
<span class="status unanswered" id="status_ps3-5-check_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_4_1" class="answer"/>
<div id="display_ps3-5-check_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_4_1_dynamath" name="input_ps3-5-check_4_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">5(b)</b> Give the probabilities to 3 significant digits. </p>
<p>
[mathjaxinline]P(X \le \mu ) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ps3-5-check_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_5_1" id="input_ps3-5-check_5_1" aria-describedby="status_ps3-5-check_5_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_5_1"/>
<span class="status unanswered" id="status_ps3-5-check_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_5_1" class="answer"/>
<div id="display_ps3-5-check_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_5_1_dynamath" name="input_ps3-5-check_5_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]P(X-\mu &gt; 1.5\sigma ) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 5" role="group"><div id="inputtype_ps3-5-check_6_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_6_1" id="input_ps3-5-check_6_1" aria-describedby="status_ps3-5-check_6_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_6_1"/>
<span class="status unanswered" id="status_ps3-5-check_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_6_1" class="answer"/>
<div id="display_ps3-5-check_6_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_6_1_dynamath" name="input_ps3-5-check_6_1_dynamath"/>
</div>
</div></div> </p>
<p>
[mathjaxinline]P(|X-\mu | \le 1.5\sigma ) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 6" role="group"><div id="inputtype_ps3-5-check_7_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_7_1" id="input_ps3-5-check_7_1" aria-describedby="status_ps3-5-check_7_1" value="" class="math" size="50"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_7_1"/>
<span class="status unanswered" id="status_ps3-5-check_7_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_7_1" class="answer"/>
<div id="display_ps3-5-check_7_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_7_1_dynamath" name="input_ps3-5-check_7_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">5(c)</b> Give the cdf of Y. Use the variables <tt class="tt">y</tt> and <tt class="tt">lambda</tt>. </p>
<p>
[mathjaxinline]F_ Y(y) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 7" role="group"><div id="inputtype_ps3-5-check_8_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_8_1" id="input_ps3-5-check_8_1" aria-describedby="status_ps3-5-check_8_1" value="" class="math" size="60"/>
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<div id="display_ps3-5-check_8_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_8_1_dynamath" name="input_ps3-5-check_8_1_dynamath"/>
</div>
</div></div> </p>
<p>
Give the probability that [mathjaxinline]Y \le 1/\lambda[/mathjaxinline]. You can use the variable <tt class="tt">lambda</tt> in your answer. </p>
<p>
[mathjaxinline]P(Y \le 1/\lambda ) =[/mathjaxinline] <div class="inline" tabindex="-1" aria-label="Question 8" role="group"><div id="inputtype_ps3-5-check_9_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-5-check_9_1" id="input_ps3-5-check_9_1" aria-describedby="status_ps3-5-check_9_1" value="" class="math"/>
<span class="trailing_text" id="trailing_text_ps3-5-check_9_1"/>
<span class="status unanswered" id="status_ps3-5-check_9_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ps3-5-check_9_1" class="answer"/>
<div id="display_ps3-5-check_9_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-5-check_9_1_dynamath" name="input_ps3-5-check_9_1_dynamath"/>
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Problem 6
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<p>
<b class="bf">6(a)</b>
<em>No answer checker given.</em>
</p>
<p>
In these problems there is some ambiguity about the exact time of day of the due date. The pset checker assumes all the ranges are in whole numbers, e.g. in part (b) the checker assumes the due date is at the same time on the 25th as the final is on the 18th. That is, the baby is due exactly 7 days after the final. </p>
<p><b class="bf">6(b)</b> Probability of a baby before the final (2 significant digits):<br/><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ps3-6-check_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-6-check_2_1" id="input_ps3-6-check_2_1" aria-describedby="status_ps3-6-check_2_1" value="" class="math" size="50"/>
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<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<div id="display_ps3-6-check_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-6-check_2_1_dynamath" name="input_ps3-6-check_2_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">6(c)</b> Probability of a baby from May 19 through May 31 (2 significant digits):<br/><div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ps3-6-check_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-6-check_3_1" id="input_ps3-6-check_3_1" aria-describedby="status_ps3-6-check_3_1" value="" class="math" size="50"/>
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<div id="display_ps3-6-check_3_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ps3-6-check_3_1_dynamath" name="input_ps3-6-check_3_1_dynamath"/>
</div>
</div></div> </p>
<p><b class="bf">6(d)</b> Give the day in May (e.g. 8,9,10,11, &#8230;) for 95% probability:<br/><div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ps3-6-check_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="text-input-dynamath_data inline" data-preprocessor="MJxPrep"/>
<div class="script_placeholder" data-src="/assets/courseware/v1/12474df7814ecb7a9a4088614ed78d4c/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/MJxPrep.js"/>
<div class="unanswered inline">
<input type="text" name="input_ps3-6-check_4_1" id="input_ps3-6-check_4_1" aria-describedby="status_ps3-6-check_4_1" value="" class="math" size="50"/>
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