Definition: Joint probability distribution

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Probability distributions ▷ Joint distribution

Definition: Let $X$ and $Y$ be random variables with sets of possible outcomes $\mathcal{X}$ and $\mathcal{Y}$. Then, a joint distribution of $X$ and $Y$ is a probability distribution that specifies the probability of the event that $X = x$ and $Y = y$ for each possible combination of $x \in \mathcal{X}$ and $y \in \mathcal{Y}$.

• The joint distribution of two scalar random variables is called a bivariate distribution.

• The joint distribution of a random vector is called a multivariate distribution.

• The joint distribution of a random matrix is called a matrix-variate distribution.

 

Sources:

• Wikipedia (2020): "Joint probability distribution"; in: Wikipedia, the free encyclopedia, retrieved on 2020-05-17; URL: https://en.wikipedia.org/wiki/Joint_probability_distribution.

Metadata: ID: D56 | shortcut: dist-joint | author: JoramSoch | date: 2020-05-17, 20:43.