Discrete Random Variables

Definition

Definition 16 (Countable Set)

A countable set is a set that can be put into a one-to-one correspondence with the natural numbers $\mathbb{N}$.

Sets such as $\mathbb{N}$, $\mathbb{Z}$ and $\mathbb{Q}$ are countable while intervals in the real space $\mathbb{R}$ are not.

Definition 17 (Discrete Random Variables)

A discrete random variable $X$ is a random variable1 whose range is a countable set.

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1

See Definition 14 for the definition of a random variable.