Definition:Marginal Probability Mass Function

Definition
Let $\left({\Omega, \Sigma, \Pr}\right)$ be a probability space.

Let $X: \Pr \to \R$ and $Y: \Pr \to \R$ both be discrete random variables on $\left({\Omega, \Sigma, \Pr}\right)$.

Let $p_{X, Y}$ be the joint probability mass function of $X$ and $Y$.

Then the probability mass functions $p_X$ and $p_Y$ are called the marginal (probability) mass functions of $X$ and $Y$ respectively.

The marginal mass function can be obtained from the joint mass function: