Discrete probability distribution

For a random variable that takes isolated values, all the probabilistic information lies in a list: which values it can take and with what probability each of them.

Definition — Probability distribution

A discrete random variable $X$ takes the values $x_1, x_2, \ldots$ with probabilities $p_1, p_2, \ldots$ (with $\sum p_i = 1$). The list $\{(x_i, p_i)\}$ is called the probability distribution.

The condition $\sum_i p_i = 1$ is essential: it expresses the certainty that one of the outcomes occurs. From this list one derives all the summary indices of the distribution (mean, variance, standard deviation).

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Topics: Probability distributions
Concepts: Probability distribution · Random variable