From ced38f14d1e84a590ae26b48e5180094469b6d1e Mon Sep 17 00:00:00 2001
From: phidias <phidias@aperx.org>
Date: Sun, 28 Dec 2025 19:57:29 +0000
Subject: [PATCH] docs: update education/statistics/random-variable

---
 education/statistics/random-variable.html | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/education/statistics/random-variable.html b/education/statistics/random-variable.html
index 5bf2490..24bc7ac 100644
--- a/education/statistics/random-variable.html
+++ b/education/statistics/random-variable.html
@@ -2,7 +2,7 @@
 title: 隨機變數 (Random Variable)
 description: 
 published: true
-date: 2025-12-28T19:56:54.087Z
+date: 2025-12-28T19:57:28.976Z
 tags: 
 editor: ckeditor
 dateCreated: 2025-12-28T16:41:51.938Z
@@ -130,7 +130,7 @@ dateCreated: 2025-12-28T16:41:51.938Z
       <tr>
         <td style="text-align:center;">
           <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Conditional Probability</strong></span></p>
-          <p><span style="font-family:Arial, Helvetica, sans-serif;">The probabilistic properties of the random variable X under the knowledge provided by the value of Y.</span></p>
+          <p><span style="font-family:Arial, Helvetica, sans-serif;">The probabilistic properties of the random variable <strong>X</strong> under the knowledge provided by the value of <strong>Y</strong>.</span></p>
         </td>
         <td>
           <figure class="image"><img src="data:image/png;base64,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"></figure>
@@ -142,7 +142,7 @@ dateCreated: 2025-12-28T16:41:51.938Z
       <tr>
         <td style="text-align:center;">
           <p><span style="font-family:Arial, Helvetica, sans-serif;"><strong>Independence</strong></span></p>
-          <p><span style="font-family:Arial, Helvetica, sans-serif;">Two random variables X and Y are said to be independent if:</span></p>
+          <p><span style="font-family:Arial, Helvetica, sans-serif;">Two random variables <strong>X</strong> and <strong>Y</strong> are said to be independent if:</span></p>
         </td>
         <td>
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