docs: update education/statistics/random-variable

education/statistics/random-variable.html

@@ -2,7 +2,7 @@
 title: 隨機變數 (Random Variable)
 description: 
 published: true
-date: 2025-12-28T19:37:25.811Z
+date: 2025-12-28T19:38:38.698Z
 tags: 
 editor: ckeditor
 dateCreated: 2025-12-28T16:41:51.938Z
@@ -29,7 +29,7 @@ dateCreated: 2025-12-28T16:41:51.938Z
   <table>
     <tbody>
       <tr>
-        <td style="width:300px;">&nbsp;</td>
+        <td style="text-align:center;width:300px;"><strong>Distribution Function</strong></td>
         <td style="text-align:center;width:300px;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Discrete</strong></span></td>
         <td style="text-align:center;width:300px;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Continuous</strong></span></td>
       </tr>
@@ -57,7 +57,7 @@ dateCreated: 2025-12-28T16:41:51.938Z
         </td>
       </tr>
       <tr>
-        <td style="text-align:center;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Marginal Probability Distributions</strong></span></td>
+        <td style="text-align:center;"><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Marginal Probability</strong></span></td>
         <td>
           <figure class="image"><img src="data:image/png;base64,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"></figure>
         </td>
@@ -66,13 +66,18 @@ dateCreated: 2025-12-28T16:41:51.938Z
         </td>
       </tr>
       <tr>
-        <td>&nbsp;</td>
-        <td>&nbsp;</td>
-        <td>&nbsp;</td>
+        <td style="text-align:center;"><strong>Conditional Probability</strong></td>
+        <td>
+          <figure class="image"><img src="data:image/png;base64,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 truncated
+        </td>
+        <td>
+          <figure class="image"><img src="data:image/png;base64,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"></figure>
+        </td>
       </tr>
     </tbody>
   </table>
 </figure>
+<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>