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2026-08-01 15:00:14 +00:00
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knowl/xref/example-uniform-EV.html
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<meta name="robots" content="noindex, nofollow">
</head>
<body class="ignore-math">
<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">3.1.7</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
</h4>
</h2>
<div class="para logical">
<div class="para">Let <span class="process-math">\(X\)</span> be uniform on the interval <span class="process-math">\([a, b]\text{.}\)</span> So <span class="process-math">\(X\)</span> has the pdf <span class="process-math">\(f(x) = \frac{1}{b - a}\text{.}\)</span> We might reasonably expect that the average value of <span class="process-math">\(X\)</span> would be the midpoint of the interval. Let’s check that:</div>
<div class="displaymath process-math">
@@ -33,8 +33,9 @@
\amp = \frac{a + b}{2}.
\end{align*}
</div>
<div class="autopermalink" data-description="Paragraph"><a href="#example-uniform-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-uniform-EV-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="Example 3.1.7"><a href="#example-uniform-EV" title="Copy heading and permalink for Example 3.1.7" aria-label="Copy heading and permalink for Example 3.1.7">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-uniform-EV">in-context</a></span>
<div class="autopermalink" aria-hidden="true" data-description="Example 3.1.7"><a tabindex="-1" href="#example-uniform-EV" title="Copy heading and permalink for Example 3.1.7" aria-label="Copy heading and permalink for Example 3.1.7">🔗</a></div>
</article><span class="incontext"><a class="internal" href="sec-Expected-Value.html#example-uniform-EV">In Context</a></span>
</body>
</html>