872 B
872 B
title, description, published, date, tags, editor, dateCreated
| title | description | published | date | tags | editor | dateCreated |
|---|---|---|---|---|---|---|
| 隨機變數 (Random Variable) | true | 2025-12-28T17:12:39.067Z | 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 \leq p_i \leq 1 and \sum_{p_i} = 1
Probability
P(X = x) = p_i
Cumulative Distribution Function (CDF)
F(X) = P(X \leq x)
F(X) = \sum_{y : y \leq x} P(X = y)
Continuous
Probability Density Function (PDF)
Probabilistic properties of a continuous random variable.
\int f(x) \,dx\ = 1
Cumulative Distribution Function (CDF)
F(X) = P(X \leq x) = \int_{-\infty}^{x} f(y) \,dy\\
f(X) = \frac{dF(x)}{dx}
P(a < x \leq b) = P(X \leq b) - P(X \leq a) = F(b) - F(a)
P(a < x \leq b) = P(a \leq x \leq b)