33 lines
2.6 KiB
HTML
33 lines
2.6 KiB
HTML
<!--
|
|
title: 隨機變數 (Random Variable)
|
|
description:
|
|
published: true
|
|
date: 2025-12-28T17:21:51.875Z
|
|
tags:
|
|
editor: ckeditor
|
|
dateCreated: 2025-12-28T16:41:51.938Z
|
|
-->
|
|
|
|
<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> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Expectation</span><br> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Cumulative Distribution Function (CDF)</span></h3>
|
|
<p><br> </p>
|
|
<h2><span style="font-family:Arial, Helvetica, sans-serif;">Continuous</span></h2>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Probability Density Function (PDF)</span></h3>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Probabilistic properties of a continuous random variable.</span></p>
|
|
<p> </p>
|
|
<p><span style="font-family:Arial, Helvetica, sans-serif;">Expectation</span><br> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Cumulative Distribution Function (CDF)</span></h3>
|
|
<p><br><br><br> </p>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Symmetric</span></h3>
|
|
<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>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Median and Quantiles</span></h3>
|
|
<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>
|
|
<h3><span style="font-family:Arial, Helvetica, sans-serif;">Variance</span></h3>
|
|
<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>
|
|
<p> </p>
|