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<article class="example example-like"><h4 class="heading">
<article class="example example-like"><h2 class="heading">
<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1.3</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
</h4>
<div class="para">Suppose we roll a fair 6-sided die two times, and let <span class="process-math">\(S\)</span> be the sum of the rolls. It’s straightforward to check the distribution for <span class="process-math">\(S\)</span> shown below. We’ve also included a column containing the products <span class="process-math">\(k \Pr(S = k)\text{,}\)</span> which must be summed up to find <span class="process-math">\(\E(S)\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#example-EV-sum-2-dice-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div> <figure class="table table-like"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1.4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" data-description="Table 3.1.4: "><a href="#example-EV-sum-2-dice-1-2" title="Copy heading and permalink for Table 3.1.4: " aria-label="Copy heading and permalink for Table 3.1.4: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
</h2>
<div class="para">Suppose we roll a fair 6-sided die two times, and let <span class="process-math">\(S\)</span> be the sum of the rolls. It’s straightforward to check the distribution for <span class="process-math">\(S\)</span> shown below. We’ve also included a column containing the products <span class="process-math">\(k \Pr(S = k)\text{,}\)</span> which must be summed up to find <span class="process-math">\(\E(S)\text{.}\)</span><div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-EV-sum-2-dice-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<figure class="table table-like"><figcaption><span class="type">Table</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1.4<span class="period heading-divison-mark heading-divison-mark__period">.</span></span><span class="space heading-divison-mark heading-divison-mark__space"> </span><div class="autopermalink" aria-hidden="true" data-description="Table 3.1.4: "><a tabindex="-1" href="#example-EV-sum-2-dice-1-2" title="Copy heading and permalink for Table 3.1.4: " aria-label="Copy heading and permalink for Table 3.1.4: ">🔗</a></div></figcaption><div class="tabular-box natural-width"><table class="tabular">
<tr class="header-horizontal">
<th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(k\)</span></th>
<th scope="col" class="c m b1 r0 l0 t0 lines"><span class="process-math">\(\Pr(S = k)\)</span></th>
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<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(1/36\)</span></td>
<td class="c m b0 r0 l0 t0 lines"><span class="process-math">\(12/36\)</span></td>
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</table></div></figure> <div class="para">The sum of the third column gives <span class="process-math">\(\E(S) = \frac{252}{36} = 7\text{.}\)</span><div class="autopermalink" data-description="Paragraph"><a href="#example-EV-sum-2-dice-1-3" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</table></div>
</figure>
<div class="para">The sum of the third column gives <span class="process-math">\(\E(S) = \frac{252}{36} = 7\text{.}\)</span><div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-EV-sum-2-dice-1-3" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
</div>
<div class="autopermalink" data-description="Example 3.1.3"><a href="#example-EV-sum-2-dice" title="Copy heading and permalink for Example 3.1.3" aria-label="Copy heading and permalink for Example 3.1.3">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-EV-sum-2-dice">in-context</a></span>
<div class="autopermalink" aria-hidden="true" data-description="Example 3.1.3"><a tabindex="-1" href="#example-EV-sum-2-dice" title="Copy heading and permalink for Example 3.1.3" aria-label="Copy heading and permalink for Example 3.1.3">🔗</a></div>
</article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-EV-sum-2-dice">In Context</a></span>
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</html>