diff --git a/education/statistics/random-variable.html b/education/statistics/random-variable.html index 07b3cf9..91faad9 100644 --- a/education/statistics/random-variable.html +++ b/education/statistics/random-variable.html @@ -2,34 +2,36 @@ title: 隨機變數 (Random Variable) description: published: true -date: 2025-12-28T19:20:55.599Z +date: 2025-12-28T19:24:32.966Z tags: editor: ckeditor dateCreated: 2025-12-28T16:41:51.938Z --> -

Discrete

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Probability Mass Function (PMF)

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Discrete

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Probability Mass Function (PMF)

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

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0 ≤ pi ≤ 1 and ∑ pi = 1

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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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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)

Probabilistic properties of a continuous random variable.

Expectation

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Cumulative Distribution Function (CDF)

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Symmetric

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Cumulative Distribution Function (CDF)

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Symmetric

If there is a point that,

Then,

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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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.