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<article class="example example-like"><h4 class="heading">
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.1.11</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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<div class="para">Suppose <span class="process-math">\(S \sim \Bin(n, p)\text{.}\)</span> <a href="sec-Discrete-RVs.html#def-binomial-distribution" class="xref" data-knowl="./knowl/xref/def-binomial-distribution.html" data-reveal-label="Reveal" data-close-label="Close" title="Definition 2.1.6">Definition 2.1.6</a> describes a binomially distributed random variable as counting the number of occurrences of some event, which either happens or not in each of <span class="process-math">\(n\)</span> independent trials. This leads us to a very natural idea: identify each individual possible occurrence of the event, and assign it an indicator random variable. In this case, let <span class="process-math">\(H_i\)</span> indicate that flip <span class="process-math">\(i\)</span> comes up heads. Then</div>
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<div class="para">Remember this formula! We’ll make frequent use of it.</div>
<div class="autopermalink" data-description="Paragraph"><a href="#example-binomial-EV-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
<div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-binomial-EV-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="Example 3.1.11"><a href="#example-binomial-EV" title="Copy heading and permalink for Example 3.1.11" aria-label="Copy heading and permalink for Example 3.1.11">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-binomial-EV">in-context</a></span>
<div class="autopermalink" aria-hidden="true" data-description="Example 3.1.11"><a tabindex="-1" href="#example-binomial-EV" title="Copy heading and permalink for Example 3.1.11" aria-label="Copy heading and permalink for Example 3.1.11">🔗</a></div>
</article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-binomial-EV">In Context</a></span>
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