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隨機變數 (Random Variable) true 2025-12-28T19:20:34.516Z markdown 2025-12-28T16:41:51.938Z

Discrete

Probability Mass Function (PMF)

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

0 ≤ pi ≤ 1 and ∑ pi = 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.