Probability distributions equations

Memorize equations for P(y=y), mean, and variance of the following distributions: Binomial, Geometric, Negative Binomial, Hypergeometric, and Possion,

p(Y=y) in a binomial distribution

(n y) (p)^y (1-p)^(n-y)

Mean (E(Y)) of binomial distribution

np

Variance (Var(Y)) of binomial

np(1-p)

p(Y=y) in a geometric distribution

p(1-p)^(y-1)

Mean (E(Y)) of geometric distribution

1/p

Variance (Var(Y)) of geometric distribution

(1-p)/p²

p(Y=y) in a negative binomial distribution

(y-1 r-1) (p)^r (1-p)^(y-r)

Mean (E(Y)) of negative binomial distribution

r/p

Variance (Var(Y)) of negative binomial distribution

(r(1-p))/p²

p(Y=y) in a hypergeometric distribution

(K k) (N-K n-k) / (N n)

Mean (E(Y)) of hypergeometric distribution

nK/N

Variance (Var(Y)) of hypergeometric distribution

n(K/N)(N-K/N)(N-n N-1)

p(Y=y) in a Possion distribution

(λ^y e^-λ)/y!

Mean (E(Y)) of Possion distribution

λ

Variance (Var(Y)) of Possion distribution

λ