From 09c0470adcfd26418b437d630038065bbf229699 Mon Sep 17 00:00:00 2001 From: phidias Date: Sun, 28 Dec 2025 17:19:57 +0000 Subject: [PATCH] docs: update education/statistics/random-variable --- education/statistics/random-variable.md | 87 +++++++++++-------------- 1 file changed, 37 insertions(+), 50 deletions(-) diff --git a/education/statistics/random-variable.md b/education/statistics/random-variable.md index b2fa5eb..03f8c0e 100644 --- a/education/statistics/random-variable.md +++ b/education/statistics/random-variable.md @@ -2,58 +2,45 @@ title: 隨機變數 (Random Variable) description: published: true -date: 2025-12-28T17:19:30.971Z +date: 2025-12-28T17:19:56.595Z tags: editor: markdown dateCreated: 2025-12-28T16:41:51.938Z --- -## Discrete - -### Probability Mass Function (PMF) - -A set of probability value **p~i~** assigned to each of the values taken by the discrete random variables **x~i~**. - -and - -Probability - -Expectation - -### Cumulative Distribution Function (CDF) - - - -## Continuous - -### Probability Density Function (PDF) - -Probabilistic properties of a continuous random variable. - -Expectation - -### Cumulative Distribution Function (CDF) - - - - - -### Symmetric - -If there is a point that, - -Then, - -Is the expectation of this random variable, equal to the point of symmetry. - -### Median and Quantiles - -The middle value of the random variable. -For median, set p to 0.5. - -### Variance - -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. - -Missing superscript or subscript argument \ No newline at end of file +

Discrete

+

Probability Mass Function (PMF)

+

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

+

and

+

Probability
+

+

Expectation
+

+

Cumulative Distribution Function (CDF)

+


+

+

Continuous

+

Probability Density Function (PDF)

+

Probabilistic properties of a continuous random variable.

+

+

Expectation
+

+

Cumulative Distribution Function (CDF)

+


+
+
+

+

Symmetric

+

If there is a point that,
+
+Then,
+
+Is the expectation of this random variable, equal to the point of symmetry.

+

Median and Quantiles

+

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

+

Variance

+

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.

+

Missing superscript or subscript argument