Probability Distributions Cheat Sheet

Means, variances and key facts for the distributions that appear in quant interviews.

Discrete

E = n p, Var = n p (1 - p)

E = \frac{1}{p}, Var = \frac{1 - p}{p ^{2}}

P (k) = \frac{e ^{- λ} λ ^{k}}{k !}, E = Var = λ

E = \frac{a + b}{2}, Var = \frac{( b - a ) ^{2}}{12}

E = \frac{1}{λ}, P (X > s + t ∣ X > s) = P (X > t)

f (x) = \frac{1}{σ 2 π} e^{- (x - μ)^{2} /2 σ^{2}}

E [U_{(k)}] = \frac{k}{n + 1}