Random variables assign numerical values to outcomes. Discrete: finite or countable values (head count). Continuous: any value in range (height, weight). Probability distribution: maps values to probabilities. Key concepts: sum of probabilities = 1 (discrete), area under curve = 1 (continuous). Common traps: confusing variable name with probability. Exam tips: identify variable type first. Expected value E(X) = Σ x × P(x): average outcome. Variance Var(X) = E(X²) - [E(X)]²: spread measure. Standard deviation σ(X) = √Var(X). Applications: investment returns, inventory optimization. Cumulative distribution: P(X ≤ x) shows probability of value or less. Moment generating functions: advanced technique. Understanding random variables foundation for statistics. Practice identifying and calculating expectations.