docs: update education/statistics/random-variable

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phidias committed 2025-12-28 19:47:44 +00:00
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title: 隨機變數 (Random Variable)
description:
published: true
date: 2025-12-28T19:45:37.395Z
date: 2025-12-28T19:47:43.526Z
tags:
editor: ckeditor
dateCreated: 2025-12-28T16:41:51.938Z
@@ -24,6 +24,13 @@ dateCreated: 2025-12-28T16:41:51.938Z
<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>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Covariance</span></h3>
<p>Independent random variables have a covariance of zero.</p>
<figure class="image"><img 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truncated
<figure class="image"><img src="data:image/png;base64,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 truncated
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p>&nbsp;</p>
<p>&nbsp;</p>
<figure class="table">
<table>
@@ -34,7 +41,10 @@ dateCreated: 2025-12-28T16:41:51.938Z
<td style="text-align:center;width:500px;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Continuous</strong></span></td>
</tr>
<tr>
<td style="text-align:center;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Probability</strong></span><br><br><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></td>
<td style="text-align:center;">
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Probability</strong></span></p>
<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>
</td>
<td>
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Probability Mass Function (PMF)</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
@@ -53,7 +63,10 @@ dateCreated: 2025-12-28T16:41:51.938Z
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<td style="text-align:center;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Cumulative</strong></span><br><br><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></td>
<td style="text-align:center;">
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Cumulative</strong></span></p>
<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>
</td>
<td>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<figure class="image"><img src="data:image/png;base64,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"></figure>
@@ -88,7 +101,10 @@ dateCreated: 2025-12-28T16:41:51.938Z
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<td style="text-align:center;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Marginal Probability</strong></span><br><br>Obtained by summing or integrating the joint probability distribution over the values of the other random variable.</td>
<td style="text-align:center;">
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Marginal Probability</strong></span></p>
<p>Obtained by summing or integrating the joint probability distribution over the values of the other random variable.</p>
</td>
<td>
<figure class="image"><img src="data:image/png;base64,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"></figure>
</td>
@@ -97,7 +113,10 @@ dateCreated: 2025-12-28T16:41:51.938Z
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<td style="text-align:center;"><strong>Conditional Probability</strong><br><br>The probabilistic properties of the random variable X under the knowledge provided by the value of Y.</td>
<td style="text-align:center;">
<p><strong>Conditional Probability</strong></p>
<p>The probabilistic properties of the random variable X under the knowledge provided by the value of Y.</p>
</td>
<td>
<figure class="image"><img src="data:image/png;base64,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 truncated
</td>
@@ -105,6 +124,20 @@ dateCreated: 2025-12-28T16:41:51.938Z
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKQAAAAzCAMAAAAuCFOIAAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGaQAGa2OgAAOgA6Ojo6OjpmOjqQOmaQOma2OpDbZgAAZjoAZjo6ZjpmZmZmZma2ZpDbZrbbZrb/kDoAkDo6nGYAkGY6kLbbkLb/kNvbkNv/tmYAtmY6tpA6ttvbttv/tv//25A625Bm27Zm27aQ29uQ2//b2////7Zm/9uQ/9u2/9vb//+2///bW2evZAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADs0lEQVRoQ+2Y24KTMBCGodXVdl1tqact9VRQm666UOH9X82ZnAkJCVLgZnPRbZdAfiZz+DJR9DSeLDCFBS6f3zx2rkPufkyhw7LG5W0cr1BccXvvk3DZbXxTRrlerrdRvkWN8d6/QJXg1KlHnd6wLQ5cvlgcp5YYReV6xRYlYavXKZ8/pdTvfJOlRX2LB76M7zE9rpfrGAbapkq4hfL4+SmqU82uD+sFRFSVxNQxgly3h4SQqdnyRKdh/OA438O3+qA5XvnhD/VbPkNMDHn4leZIA6q16/RlbsQ53eKCvc4MIuWS2tpZvDFMQLeYMFPPIFKGgbZ2O8vgxepd0y+utJUhjxEuqQInqnatrI5OQbgLTB84VcJTOcSz+JZ/a6fC7Oa3cIE5UpCscmJxcD0wL7WbNDNk+ju22fAykydzbe9YnJPFR4wN/NRFqnlDy6JBWiFclWk5u+1smfCAqBCbXSV65EuACnF/OqdFWn6uUi5pe0CViHRZvuac2XykBKhwjW3S8oKNEQR/8wb0EoaX2f6X0HhuQG9wuZfvYBXU7UBV8uyL3wZ1Gm/svC4Byv8QPsOaGcYNRQFQwRodph8xqSmAChbpIK1Ry4NKo4EyHaSlKjJBcOTjOscUaZdAiTqbNEhrTGQxn114S5GDtLpFasbt+RWNx/wdgH15KmLIfyAS/m6hXsGHdThIa0xLcpcs13t20kRLYo2qU0fKcpGWCpyr+6SsVtmqPtBzO4gsb48R0Qsn/D9Hhs7Qug7SGjUF8U0tFq9oaUKRdbqlZR4qAB1w4ii/4rkD1atjs0Zaw7iqiSttWpGbVO1YxNDAIZbyhA7BCMVCWnBf2IEf7zeBxsSVFq0IgKoP79kJjYrkp7VG3IB5o5wdPy15u8lVnenMBJr20ww4EC5ZH/YoQlqS0Z223fAr2xYi3v8D1aRus6racKW5LdzbLztYnix/Sp+0JUvygh/iYJZBWk2u6rSj6gjxabaAa9AKByiw2M0jJEa0H01BmDBb40rF2QAaO654UoW74vATe7edfFdbQCPKcq8ukEPk+fhAI3v4MIBGtH16dYHsIqH1RQ91w4cJNBo8zdsF0l/NLPHq98xdIF0k65ophFEiZ+4C6SKZSyqEUds/bxdI18irh0IYLQXN2gWyuKRAGLikUuKsXSBdpKgICmHUfl+vCzQwCQmg0RBGanN0gQau2P92ydhENqhkZ8nRBeq/yNA7hAM2+x2AK59cXaChK/a+X3WETIRxd4F6LzLLDf8AXVNp/xcOMuAAAAAASUVORK5CYII="></figure>
</td>
</tr>
<tr>
<td style="text-align:center;">
<p><strong>Independence</strong></p>
<p>Two random variables X and Y are said to be independent if:</p>
</td>
<td>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>for all values <strong>i</strong> of X and <strong>j</strong> of Y.</p>
</td>
<td>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>for all X and Y.</p>
</td>
</tr>
</tbody>
</table>
</figure>