diff --git a/education/statistics/random-variable.md b/education/statistics/random-variable.md index 487f76e..bd8f33b 100644 --- a/education/statistics/random-variable.md +++ b/education/statistics/random-variable.md @@ -2,45 +2,62 @@ title: 隨機變數 (Random Variable) description: published: true -date: 2025-12-28T17:20:13.132Z +date: 2025-12-28T19:20:15.044Z tags: editor: markdown dateCreated: 2025-12-28T16:41:51.938Z --- -

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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and

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Probability
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Expectation
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Cumulative Distribution Function (CDF)

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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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Cumulative Distribution Function (CDF)

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Symmetric

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If there is a point that,
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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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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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Missing superscript or subscript argument

+## 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~**. + +**0 ≤ p~i~ ≤ 1 and ∑ p~i~ = 1** + +Probability + $$\\leq$$ + +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. \ No newline at end of file