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<h2 class="hd hd-2 unit-title">Central limit theorem; law of large numbers, histograms</h2>
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<h2 class="hd hd-2 unit-title">Class 6 reading questions: Central limit theorem, law of large numbers</h2>
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Remember, unless otherwise stated the checker expects your answer to 3 &#8216;significant' digits. </p>
<p><b class="bf">1.</b> True or False. A density histogram of 100000 values is <i class="it">always</i> close to the graph of the underlying density. </p>
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<p><b class="bf">2.</b> If [mathjaxinline]X[/mathjaxinline] has mean [mathjaxinline]\mu =2[/mathjaxinline] and variance [mathjaxinline]\sigma ^2=4[/mathjaxinline] then which of the following is the standardization of [mathjaxinline]X[/mathjaxinline]? </p>
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<p><b class="bf">3.</b> If [mathjaxinline]Y[/mathjaxinline] is a standard normal random variable and [mathjaxinline]W = 3Y + 4[/mathjaxinline] then what is the mean of [mathjaxinline]W[/mathjaxinline]? </p>
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<p><b class="bf">4.</b> A fair coin is tossed 64 times. Use the central limit theorem to estimate the probability of getting more that 40 heads. Use the rule of thumb probabilities for the normal distribution </p>
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<h2 class="hd hd-2 unit-title">Appendix</h2>
<div class="vert-mod">
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<div class="xblock xblock-public_view xblock-public_view-html xmodule_display xmodule_HtmlBlock" data-block-type="html" data-runtime-version="1" data-usage-id="block-v1:MITx+18.05r_10+2022_Summer+type@html+block@class6-prep-c_hashpdf" data-graded="True" data-runtime-class="LmsRuntime" data-course-id="course-v1:MITx+18.05r_10+2022_Summer" data-has-score="False" data-init="XBlockToXModuleShim" data-request-token="3385201cdb7f11efb020029b57e3cc89">
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<p>You can download this pdf file from <a href="/assets/courseware/v1/7038b2cba03ebf835caf7c2688c0b1f6/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_class6-prep-c.pdf">here</a></p><iframe src="/assets/courseware/v1/7038b2cba03ebf835caf7c2688c0b1f6/asset-v1:MITx+18.05r_10+2022_Summer+type@asset+block/pdf_mit18_05_s22_class6-prep-c.pdf" width="100%" height="1000px"> </iframe>
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