Discrete random variable

A discrete random variable is one whose possible values you could write out in a list, usually because it comes from counting something. If $X$ is the number of heads in two fair coin flips, then $X$ takes the values 0, 1, and 2 with probabilities $0.25$, $0.50$, and $0.25$. Every discrete probability distribution satisfies $\sum P(x_i) = 1$ (the probabilities sum to 1), and here $0.25 + 0.50 + 0.25 = 1$. Counts are discrete; measurements like time and weight are continuous.