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<h1 style="color:green;">Friday will be a regular class. We will do Class 10 (starting statistics). The reading is posted the reading questions are optional.</h1>
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<h2 class="hd hd-2 unit-title">Introduction to statistics</h2>
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<h2 class="hd hd-2 unit-title">Class 10 reading questions: Introduction to statistics</h2>
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<p><b class="bf">1.</b> You have experimental data [mathjaxinline]x_1,\ldots , x_ n[/mathjaxinline] drawn from a [mathjaxinline]\text {N}(0,\sigma ^2)[/mathjaxinline] distribution. </p>
<p><b class="bf">(a)</b> True or False: [mathjaxinline]\sigma[/mathjaxinline] is a statistic. </p>
<p>
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<p><b class="bf">(b)</b> True or False: The sample variance is a statistic. </p>
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<p><b class="bf">(c)</b> True or False: The sample mean is a statistic. </p>
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<text> False</text>
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<p><b class="bf">(d)</b> True or False: The sample mean will always be 0. </p>
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<text> False</text>
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<h2 class="hd hd-2 unit-title">Maximum likelihood estimates</h2>
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<h2 class="hd hd-2 unit-title">Class 10 reading questions: Maximum likelihood estimate</h2>
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<p><b class="bf">1.</b> Data is drawn from an exponential distribution with pdf [mathjaxinline]f(x) = \lambda e^{-\lambda x}[/mathjaxinline], where [mathjaxinline]\lambda[/mathjaxinline] is unknown. Given the two data points [mathjaxinline]x=1[/mathjaxinline] and [mathjaxinline]x=2[/mathjaxinline], find the maximum likelihood estimate for [mathjaxinline]\lambda .[/mathjaxinline] </p>
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<p style="display:inline">[mathjaxinline]\hat{\lambda } =[/mathjaxinline]</p>
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<p><b class="bf">2.</b> There are [mathjaxinline]n[/mathjaxinline] students in a class. They are assigned numbers 1 to [mathjaxinline]n[/mathjaxinline]. Three students are chosen at random and asked their numbers, which turn out to be 1, 3, 7. Assume that classes are allowed a maximum of 30 students. Find the maximum likelihood estimate for [mathjaxinline]n[/mathjaxinline]. (Hint, the students are drawn from a discrete uniform distribution.) </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c10-rq22_2_1">
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<input type="radio" name="input_c10-rq22_2_1" id="input_c10-rq22_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="c10-rq22_2_1-choice_1-label" for="input_c10-rq22_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_c10-rq22_2_1">
<text> 1</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c10-rq22_2_1" id="input_c10-rq22_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="c10-rq22_2_1-choice_2-label" for="input_c10-rq22_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c10-rq22_2_1">
<text> 3</text>
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<input type="radio" name="input_c10-rq22_2_1" id="input_c10-rq22_2_1_choice_3" class="field-input input-radio" value="choice_3"/><label id="c10-rq22_2_1-choice_3-label" for="input_c10-rq22_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_c10-rq22_2_1">
<text> 7</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c10-rq22_2_1" id="input_c10-rq22_2_1_choice_4" class="field-input input-radio" value="choice_4"/><label id="c10-rq22_2_1-choice_4-label" for="input_c10-rq22_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_c10-rq22_2_1">
<text> 14</text>
</label>
</div>
<div class="field">
<input type="radio" name="input_c10-rq22_2_1" id="input_c10-rq22_2_1_choice_5" class="field-input input-radio" value="choice_5"/><label id="c10-rq22_2_1-choice_5-label" for="input_c10-rq22_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_c10-rq22_2_1">
<text> 30</text>
</label>
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