From 80cab8c80a6e762725f47fbcfc5be636a481c685 Mon Sep 17 00:00:00 2001 From: phidias Date: Sun, 28 Dec 2025 19:36:36 +0000 Subject: [PATCH] docs: update education/statistics/random-variable --- education/statistics/random-variable.html | 109 ++++++++++++++-------- 1 file changed, 68 insertions(+), 41 deletions(-) diff --git a/education/statistics/random-variable.html b/education/statistics/random-variable.html index 576aca0..807c3a2 100644 --- a/education/statistics/random-variable.html +++ b/education/statistics/random-variable.html @@ -2,79 +2,106 @@ title: 隨機變數 (Random Variable) description: published: true -date: 2025-12-28T19:33:09.392Z +date: 2025-12-28T19:36:36.326Z tags: editor: ckeditor dateCreated: 2025-12-28T16:41:51.938Z --> -

General

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Symmetric

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If there is a point that,

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General

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Symmetric

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If there is a point that,

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Then,

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Then,

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Is the expectation of this random variable, equal to the point of symmetry.

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Is the expectation of this random variable, equal to the point of symmetry.

 

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Median and Quantiles

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The middle value of the random variable.
For median, set p to 0.5.

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Median and Quantiles

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The middle value of the random variable.
For median, set p to 0.5.

 

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Variance

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A positive quantity that measures the spread of the distribution of the random variable about its mean value.
Larger values of the variance indicate that the distribution is more spread out.

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Variance

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A positive quantity that measures the spread of the distribution of the random variable about its mean value.
Larger values of the variance indicate that the distribution is more spread out.

 

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Discrete

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Probability Mass Function (PMF)

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A set of probability value pi assigned to each of the values taken by the discrete random variables xi.

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 DiscreteContinuous
Jointly Distributed +
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satisfying 

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+ 		 
Joint Cumulative +
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+ 		 
Marginal Probability Distributions +
+ 		 
   
+
+

Discrete

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Probability Mass Function (PMF)

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A set of probability value pi assigned to each of the values taken by the discrete random variables xi.

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Probability

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Probability

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Expectation

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Expectation

 

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Cumulative Distribution Function (CDF)

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A set of probability value pi assigned to each of the values taken by the discrete random variables xi.

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Cumulative Distribution Function (CDF)

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A set of probability value pi assigned to each of the values taken by the discrete random variables xi.

 

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Jointly Distributed

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satisfying 

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-

 

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Joint Cumulative

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-
-

 

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Marginal Probability Distributions

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-

 

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Contin

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-

uous

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Probability Density Function (PDF)

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Probabilistic properties of a continuous random variable.

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Continuous

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Probability Density Function (PDF)

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Probabilistic properties of a continuous random variable.

 

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Expectation

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Expectation

 

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Cumulative Distribution Function (CDF)

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Probabilistic properties of a continuous random variable.

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Cumulative Distribution Function (CDF)

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Probabilistic properties of a continuous random variable.

 

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Jointly Distributed

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Jointly Distributed

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satisfying 

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satisfying 

 

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Joint Cumulative

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Joint Cumulative

 

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Marginal Probability Distributions

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Marginal Probability Distributions