55 lines
15 KiB
HTML
55 lines
15 KiB
HTML
<!--
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title: 隨機變數 (Random Variable)
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description:
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published: true
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date: 2025-12-28T19:27:09.103Z
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tags:
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editor: ckeditor
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dateCreated: 2025-12-28T16:41:51.938Z
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-->
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<h2>Discrete</h2>
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<h3>Probability Mass Function (PMF)</h3>
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<p>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>.</p>
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<figure class="image"><img src="data:image/png;base64,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">
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<figcaption>FIG 1-1</figcaption>
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</figure>
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<p><br><strong>Probability</strong></p>
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<figure class="image"><img src="data:image/png;base64,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">
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<figcaption>FIG 1-2</figcaption>
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</figure>
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<p><br><strong>Expectation</strong></p>
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<figure class="image"><img src="data:image/png;base64,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">
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<figcaption>FIG 1-3</figcaption>
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</figure>
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<p> </p>
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<h3>Cumulative Distribution Function (CDF)</h3>
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<p>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>.</p>
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<figure class="image"><img src="data:image/png;base64,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">
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<figcaption>FIG 1-4</figcaption>
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</figure>
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<figure class="image"><img src="data:image/png;base64,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">
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<figcaption>FIG 1-5</figcaption>
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</figure>
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<p> </p>
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<h2>Continuous</h2>
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<h3>Probability Density Function (PDF)</h3>
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<p>Probabilistic properties of a continuous random variable.</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p> </p>
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<p>Expectation</p>
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<p> </p>
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<h3>Cumulative Distribution Function (CDF)</h3>
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<p>Probabilistic properties of a continuous random variable.</p>
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<figure class="image"><img src="data:image/png;base64,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"></figure>
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<p> </p>
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<p> </p>
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<h3>Symmetric</h3>
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<p>If there is a point that,</p>
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<p>Then,</p>
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<p>Is the expectation of this random variable, equal to the point of symmetry.</p>
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<h3>Median and Quantiles</h3>
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<p>The middle value of the random variable.<br>For median, set p to 0.5.</p>
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<h3>Variance</h3>
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<p>A positive quantity that measures the spread of the distribution of the random variable about its mean value.<br>Larger values of the variance indicate that the distribution is more spread out.</p>
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