33 lines
2.6 KiB
HTML
33 lines
2.6 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: 2025-12-28T17:34:08.898Z
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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><span style="font-family:Arial, Helvetica, sans-serif;">Discrete</span></h2>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Probability Mass Function (PMF)</span></h3>
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<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>
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<p><strong>0 ≤ p<sub>i</sub> ≤ 1 and ∑ p<sub>i</sub> = 1</strong></p>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">Probability</span><br> </p>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">Expectation</span><br> </p>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Cumulative Distribution Function (CDF)</span></h3>
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<p><br> </p>
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<h2><span style="font-family:Arial, Helvetica, sans-serif;">Continuous</span></h2>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Probability Density Function (PDF)</span></h3>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">Probabilistic properties of a continuous random variable.</span></p>
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<p> </p>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">Expectation</span><br> </p>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Cumulative Distribution Function (CDF)</span></h3>
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<p><br><br><br> </p>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Symmetric</span></h3>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">If there is a point that,</span><br><br><span style="font-family:Arial, Helvetica, sans-serif;">Then,</span><br><br><span style="font-family:Arial, Helvetica, sans-serif;">Is the expectation of this random variable, equal to the point of symmetry.</span></p>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Median and Quantiles</span></h3>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">The middle value of the random variable.</span><br><span style="font-family:Arial, Helvetica, sans-serif;">For median, set p to 0.5.</span><br> </p>
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<h3><span style="font-family:Arial, Helvetica, sans-serif;">Variance</span></h3>
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<p><span style="font-family:Arial, Helvetica, sans-serif;">A positive quantity that measures the spread of the distribution of the random variable about its mean value.</span><br><span style="font-family:Arial, Helvetica, sans-serif;">Larger values of the variance indicate that the distribution is more spread out.</span></p>
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<p> </p>
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