D.4 Distributions
Discrete and continuous random variables. A discrete random variable X has a probability distribution: a table of values with probabilities summing to 1. Expected value E(X) = Σ x · P(X = x) is the long-run average. The BINOMIAL distribution X ~ B(n, p) models n independent identical Bernoulli trials — mean = np, variance = np(1−p). The NORMAL distribution N(μ, σ²) is the bell curve: symmetric about μ, inflection points at μ ± σ, total area = 1, with the GDC (normCDF / invNorm) handling probability calculations. Standardisation Z = (X − μ)/σ converts any normal X to the standard normal N(0, 1) — letting you compare scores across distributions and find unknown μ or σ from probability statements.
Discrete random variables and expected valueSign up
Discrete random variables and their probability distributions · Expected value E(X) = Σ x P(X = x)
Binomial distributionSign up
When is X binomial? The four BINS conditions · Binomial: P(X = k), mean = np, variance = np(1−p)
Normal distributionSign up
The bell curve: symmetric, peaked at μ, inflection at μ ± σ · Normal probabilities + inverse normal — GDC commands
Standardisation and inverse normal with unknown μ or σSign up
Standardisation: Z = (X − μ)/σ · Find unknown μ or σ from a probability statement