stat 390 - discrete random variable distributions

bernoulli distribution

a distribution of a SINGLE bernoulli trial, so has 2 outcomes

bernoulli expression

Ber(p)

binomial distribution

a frequency distribution of n successes
(totalling bernoulli trials) w same probability of success

sampling with replacement

binomial

sampling without replacement

hypergeometric

binomial expression

bin(n, p)

hypergeometric distribution

distribution of a variable that has two outcomes when probability changes due to no replacement

hypergeometric expression

HyperGeo(N, M, n)

geometric distribution

distribution that models the waiting time till the first success occurs at a given trial number

geometric expression

geo(p)

possion distribution

distribution that models independent, constant (p), and rare events

possion expression

pos(λ)

E[X] using pmf