Existence of expectation

• Not every PMF has an expectation, it does when it is absolutely summable.

• Definition: A discrete random variable $X$ is absolutely summable if $\mathbb{E}[\mid X \mid] = \displaystyle{ \sum_{ x\in X(\Omega)} } \mid x\mid \cdot p_X (x) < \infty$

• Most of the random variables we use in practice are absolutely summable.