Discrete Distribution Formulas

Binomial PMF

Binomial Expectation

np

Binomial Variance

npq

Binomial MGF

(pe^t + q)^n

Poisson PMF

Poisson Expectation & Poisson Variance

λ

Poisson MGF

Geometric PMF

p*(q^(n-1))

Geometric Expectation

1/p

Geometric Variance

q/p²

Geometric MGF

Negative Binomial PMF

Negative Binomial Expectation

r/p

Negative Binomial Variance

(rq)/p²

Negative Binomial MGF

Bernoulli PMF

p if x = 1, q if x = 0

Bernoulli Expectation

p

Bernoulli Variance

pq