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@@ -969,7 +969,19 @@ A\cap B \amp = \{HHH, HHT\}
 <div class="autopermalink" data-description="Exercise 33"><a href="#Exam-1-Review-4-32" title="Copy heading and permalink for Exercise 33" aria-label="Copy heading and permalink for Exercise 33">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-33"><h4 class="heading"><span class="codenumber">34<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
 <div class="para" id="Exam-1-Review-4-33-1-1">A continuous random variable <span class="process-math">\(X\)</span> taking values in <span class="process-math">\([1, 2]\)</span> has p.d.f. <span class="process-math">\(\displaystyle{f(x) = \frac{1}{2}\left(\frac{1}{x^2} + x\right)}\text{.}\)</span> Find <span class="process-math">\(\Var(X)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-33-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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-<div class="autopermalink" data-description="Exercise 34"><a href="#Exam-1-Review-4-33" title="Copy heading and permalink for Exercise 34" aria-label="Copy heading and permalink for Exercise 34">🔗</a></div></article><div class="autopermalink" data-description="Exercises"><a href="#Exam-1-Review-4" title="Copy heading and permalink for Exercises" aria-label="Copy heading and permalink for Exercises">🔗</a></div></section><div class="autopermalink" data-description="Section: Exam 1 Review"><a href="#Exam-1-Review" title="Copy heading and permalink for Section: Exam 1 Review" aria-label="Copy heading and permalink for Section: Exam 1 Review">🔗</a></div></section></div>
+<div class="autopermalink" data-description="Exercise 34"><a href="#Exam-1-Review-4-33" title="Copy heading and permalink for Exercise 34" aria-label="Copy heading and permalink for Exercise 34">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-34"><h4 class="heading"><span class="codenumber">35<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="Exam-1-Review-4-34-1-1">Suppose a coin has an unknown probability of coming up heads. We perform the experiment in <span class="process-math">\(n\)</span> independent trials, during which it takes <span class="process-math">\(k_1, k_2, \dotsc, k_n\)</span> flips to see our first heads in each trial. Find a "common sense" MLE formula for the geometric distribution.<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-34-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 35"><a href="#Exam-1-Review-4-34" title="Copy heading and permalink for Exercise 35" aria-label="Copy heading and permalink for Exercise 35">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-35"><h4 class="heading"><span class="codenumber">36<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="Exam-1-Review-4-35-1-1">A particular store owner wants to approximate the average hourly rate at which customers come into the store. They observe 80 customers enter during a particular 4-hour shift. What is the maximum likelihood estimation for the hourly customer rate?<div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-35-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 36"><a href="#Exam-1-Review-4-35" title="Copy heading and permalink for Exercise 36" aria-label="Copy heading and permalink for Exercise 36">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-36"><h4 class="heading"><span class="codenumber">37<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="Exam-1-Review-4-36-1-1">A radioactive material emits particles at an unknown probabilistic rate <span class="process-math">\(\lambda\)</span> particles per minute. We observe particles emitted at times 1.1, 1.7, 1.3, 2.2, 1.9, and 1.8 minutes. Write the likelihood function <span class="process-math">\(\mathcal{L}(\lambda)\)</span> based on this data. What is the maximum likelihood estimation for <span class="process-math">\(\lambda\text{?}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-36-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 37"><a href="#Exam-1-Review-4-36" title="Copy heading and permalink for Exercise 37" aria-label="Copy heading and permalink for Exercise 37">🔗</a></div></article><article class="exercise exercise-like" id="Exam-1-Review-4-37"><h4 class="heading"><span class="codenumber">38<span class="period heading-divison-mark heading-divison-mark__period">.</span></span></h4>
+<div class="para" id="Exam-1-Review-4-37-1-1">Suppose a parameter <span class="process-math">\(\theta\)</span> takes values in <span class="process-math">\([0, 1]\)</span> with likelihood function <span class="process-math">\(\mathcal{L}(\theta) = \sqrt{\theta} - \theta^2\text{.}\)</span> Find the maximum likelihood estimation of <span class="process-math">\(\theta\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#Exam-1-Review-4-37-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
+</div>
+<div class="autopermalink" data-description="Exercise 38"><a href="#Exam-1-Review-4-37" title="Copy heading and permalink for Exercise 38" aria-label="Copy heading and permalink for Exercise 38">🔗</a></div></article><div class="autopermalink" data-description="Exercises"><a href="#Exam-1-Review-4" title="Copy heading and permalink for Exercises" aria-label="Copy heading and permalink for Exercises">🔗</a></div></section><div class="autopermalink" data-description="Section: Exam 1 Review"><a href="#Exam-1-Review" title="Copy heading and permalink for Section: Exam 1 Review" aria-label="Copy heading and permalink for Section: Exam 1 Review">🔗</a></div></section></div>
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