5.4.1—Discrete random variables

A discrete random variable takes separate values with probabilities p(x)≥0 and Σp(x)=1. Its probability table defines the sample space and supports expectation calculations.

Check the support and total probability before using formulas. A probability mass at one value is not a continuous density over an interval.

For X=0,1,2 with probabilities 0.2,0.5,0.3, the probabilities sum to 1 and describe every possible outcome.

A discrete variable can have many values; “discrete” means countable separated outcomes, not necessarily only two.