Probability Distributions Flashcards

Grade 11 · Math · Flashcards

Essential vocabulary and formulas for probability distributions, binomial, and normal distributions.

Flashcards

Random variable: A variable that takes on numerical values determined by a random experiment
Discrete random variable: Takes countable values (0, 1, 2, ...); probabilities given by PMF
Continuous random variable: Takes any value in an interval; probabilities are areas under PDF curve
Expected value E(X): Σ x·P(x); the long-run average value of a random variable
Variance Var(X): E(X²) - [E(X)]²; measure of spread around the mean
Standard deviation σ: √Var(X); measures spread in same units as the random variable
Binomial distribution: n independent trials, constant probability p; counts successes X ~ B(n,p)
Binomial formula: P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Binomial mean: μ = np
Binomial variance: σ² = np(1-p)
Normal distribution: Symmetric bell curve fully described by μ and σ; X ~ N(μ, σ²)
Empirical rule: 68% within μ±σ; 95% within μ±2σ; 99.7% within μ±3σ
Z-score formula: z = (x - μ) / σ; measures distance from mean in standard deviations