Definition:Convolution of Probability Distributions

Definition

Let $X$ and $Y$ be independent random variables.

Let $Z = X + Y$.

The probability distribution of $Z$ is called the convolution of the probability distributions of $X$ and $Y$.

Sources

• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $3.9$: Functions of Two or More Random Variables: Definition $3.9.1$