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2025-12-28 19:43:20 +00:00
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title: 隨機變數 (Random Variable)
description:
published: true
date: 2025-12-28T19:40:00.675Z
date: 2025-12-28T19:43:19.699Z
tags:
editor: ckeditor
dateCreated: 2025-12-28T16:41:51.938Z
@@ -33,6 +33,25 @@ dateCreated: 2025-12-28T16:41:51.938Z
<td style="text-align:center;width:500px;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Discrete</strong></span></td>
<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></td>
<td>
<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>&nbsp;</p>
<figure class="image"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOIAAAApCAMAAAAf4QWSAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZjoAZjo6ZpDbZrbbZrb/kDoAkDpmkGY6kGZmkLbbkLb/kNv/tmYAtmY6tpA6tpBmtpCQtrZmttvbttv/tv/btv//25A627Zm27aQ2////7Zm/9uQ/9u2/9vb//+2///bfF5H2gAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADPklEQVRoQ+1Z0XbaMAy1M4a3rl0ZgdGMbg1lHVsWEhr//7/NsgM4sgymkJ3AwU89RpbvtXUlOWXsOq4ncD2BQ06g4OSIng5x0nHblPN3f5oY5TO/KIpVzHkfX0N6URRZKTh/QByLy6LIMu7EZfnhkrTImEw4f7/seMo4Eh7IcXikj64vh8qB5dh1zIfiU3LEleNQF123Bzk6laProA/Ed2FyVIXQTaBKjievhX9VxR2cMlWvpqGhVgoif55Cjk0IWTRhuaBA5dPgBG6ZrqbhaioFkT6PlyOCUMXALsWpWuZjfvs9SEdN0/L2l3EZMuj2jGrkQrytbTCEQpMrGhVX/hwF8yNMwylmdC9zvBwbEEwrX24j9XV+g/nJuYie5IxHKKwIUzhJRHE15vzu5W658fIDjGD288hz3epdhcj7IHhul6S4cZlFX3DuySalmDwuZIKqMmHqUixEf6ka7CGrvVQxbLWZJTEqOaKs6oGgUtNm2ImDoGj21eN1LtwoLcWteq3ixxtpim6xZqTloL3o3etZb3UohNPj0BDCb9GiqBZJJ1YzDZF4n7qmiKJZmWky+m9dKOpZX68mE5e8FwLFsnmL9fkiVci8kXFSuGQdqG4SRKZNinVw6/UsBUrgwMzKxPdygrjGYxcEx7hB0RxOM6PWK/LxeiOZwAlYOQn73JqidGPCw6w0XoDnetZTdwuiTaUhBGnR7G4CyTtMFwJxmga85+wj1GTkVJd47UVDtWfdTauYCOC3Q4CqP1GbD3YxVJfcX6qvYQpnFe9/zpViG4AqJBfy8YU/5APlRTvor779tmbdjclPUm+HoI71WfDo63Yj6u7TnurKerqAfrS+A1KmcnoDafzT2mM54veLagRdsJYim/HeglmzDkVKiOomaAjUzWAIO2+v/tHoQI+i9W8rtOLbhlDFm7yQhrafIUdH2ZBChPhuF4LpY2HIZJjr/qu14TwI6uhpGUJmdAhjxgetsQPHtBBh/r9BaJUf1JXWtd4yg33uPULct+ycfneFaGXScyLixUoIMfx5fRYnQAmRalfPggwJkhLiahTQE58PZfU1gxrBXwG7z9RueG2q+9v+7nNb9030JR79j6p/f0dVE36qbmkAAAAASUVORK5CYII="></figure>
<p><br><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Probability</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><br><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Expectation</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
</td>
<td>
<p><span style="font-family:Arial, Helvetica, sans-serif;">Probabilistic properties of a continuous random variable.</span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Expectation</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
</td>
</tr>
<tr>
<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>
@@ -92,18 +111,7 @@ dateCreated: 2025-12-28T16:41:51.938Z
<p>&nbsp;</p>
<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>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><br><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Probability</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p><br><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Expectation</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</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>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>
<p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Expectation</strong></span></p>
<figure class="image"><img src="data:image/png;base64,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"></figure>
<p>&nbsp;</p>