Definition: Conditional probability distribution

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

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

 

Sources:

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

Metadata: ID: D58 | shortcut: dist-cond | author: JoramSoch | date: 2020-05-17, 21:25.