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docs: update education/statistics/random-variable

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2025-12-28 17:25:17 +00:00
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education/statistics/random-variable.html
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title: 隨機變數 (Random Variable)
description:
published: true
date: 2025-12-28T17:21:51.875Z
date: 2025-12-28T17:25:16.524Z
tags:
editor: ckeditor
dateCreated: 2025-12-28T16:41:51.938Z
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<h2><span style="font-family:Arial, Helvetica, sans-serif;">Discrete</span></h2>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Probability Mass Function (PMF)</span></h3>
<p><span style="font-family:Arial, Helvetica, sans-serif;">A set of probability value <strong>p<sub>i</sub></strong> assigned to each of the values taken by the discrete random variables <strong>x<sub>i</sub></strong>.</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">and</span></p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Probability</span><br>&nbsp;</p>
<p>$0 \leq p_i \leq 1$ and $\sum_{p_i} = 1$</p>
<p><br><span style="font-family:Arial, Helvetica, sans-serif;">Probability</span><br>$P(X = x) = p_i$</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Expectation</span><br>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Cumulative Distribution Function (CDF)</span></h3>
<p><br>&nbsp;</p>