Discrete Random Variables#
Definition#
Definition 74 (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 \(\R\) are not.
Definition 75 (Discrete Random Variables)
A discrete random variable \(X\) is a random variable[1] whose range is a countable set.