SL 4.7—Discrete random variables

Discrete Random Variable: A variable whose value is determined by the outcome of a random process, and which can only take a countable set of specific, separate values , typically whole numbers.

Think of rolling a standard six-sided die. The result can only be 1, 2, 3, 4, 5, or 6 , nothing in between. This makes it a classic discrete random variable, usually written as $X$.

We use capital letters like $X$ for the random variable itself, and lowercase letters like $x$ for specific values it can take. So we write $P(X=x)$ to mean "the probability that $X$ takes the value $x$".