Random variable X assigns numerical values to outcomes. Discrete: countable values (0,1,2,...). Continuous: any value in interval. Probability distribution: P(X=x) for discrete; f(x) for continuous (probability density). Expected value E(X) = Σ[x × P(x)] for discrete; ∫xf(x)dx for continuous. Variance Var(X) = E(X²) - [E(X)]². Example: Roll die. X = number. E(X) = 1×(1/6) + 2×(1/6) + ... + 6×(1/6) = 3.5. Var(X) = E(X²) - 12.25 = 91/6 - 12.25 ≈ 2.92. Solving: Define random variable. Calculate probabilities. Compute expected value and variance. Exam tip: Understand discrete vs continuous. Use variance for risk assessment.