wiki/education/statistics/random-variable.md

title, description, published, date, tags, editor, dateCreated

title	description	published	date	tags	editor	dateCreated
隨機變數 (Random Variable)		true	2025-12-28T17:20:13.132Z		markdown	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.