37 lines
2.1 KiB
HTML
Executable File
37 lines
2.1 KiB
HTML
Executable File
<!DOCTYPE html>
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<html lang="en-US" dir="ltr">
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<!--******************************************-->
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<!--* Authored with PreTeXt *-->
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<!--* pretextbook.org *-->
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<!--* Theme: boulder *-->
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<!--* Generated from PreTeXt source *-->
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<!--* https://pretextbook.org *-->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
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<meta name="robots" content="noindex, nofollow">
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</head>
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<body class="ignore-math">
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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">3.1.5</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h4>
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<div class="para logical">
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<div class="para">Let <span class="process-math">\(X\)</span> indicate an event <span class="process-math">\(A\)</span> which has probability <span class="process-math">\(p\text{.}\)</span> Then:</div>
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<div class="displaymath process-math">
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\begin{gather*}
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\E(X) = 0 \cdot (1-p) + 1 \cdot p = p.
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\end{gather*}
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</div>
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<div class="para">That is, the expected value of an indicator random variable is the probability of the event that it indicates.</div>
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<div class="autopermalink" data-description="Paragraph"><a href="#example-indicator-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>
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<div class="autopermalink" data-description="Example 3.1.5"><a href="#example-indicator-EV" title="Copy heading and permalink for Example 3.1.5" aria-label="Copy heading and permalink for Example 3.1.5">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-indicator-EV">in-context</a></span>
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</body>
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</html>
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