Formula Sheet x = 1 n Pn k=1 s2 = xk 1 n1 Pn k=1 (x x)2 IQR = Q3 Q1 Probability: P (Ac ) = 1 P (A) P (A B) = P (A) + P (B) P (A B) Conditional probability: P (A|B) = P (AB) P (B) P (A B) = P (A)P (B|A) Law of total probability: P (A) = P (A B) + P (A B c ) Independence: P (A B) = P (A)P (B) or P (A|B) = P (A) or P (B|A) = P (B) Disjoint: A B = and P (A B) = 0 Random variables: P = E(X) = x xf (x) P E(g(X)) = x g(x)f (x) E(aX + b) = aE(X) + b \u00012 P P xf (x) 2 = V ar(X) = E(X 2 ) E(X)2 = x x2 f (x) x p 2 V ar(aX + b) = a V ar(X) SD(X) = V ar(X) \u0012 \u0013 n Binomial distribution: X Bin(n, p) with PMF P (X = x) = px (1 p)nx x E(X) = np V ar(X) = np(1 p) HyperGeom: X HypGeo(N, n, p) with PMF P (X = x) = m x E(X) = np V ar(X) = N n np(1 N 1 p). N m nx N n where m = N p