Probability Distributions (Parameters, PDF, MGF)

X ~ U(N)

Discrete Uniform Parameter(s)

Discrete Uniform PDF

Discrete Uniform MGF

X ~ Bi(n=1, p)

Bernoulli Parameter(s)

Bernoulli PDF

Bernoulli MGF

X ~ Bi(n,p)

Binomial PDF

Binomial MGF

X ~ Hyp(k,m,n)

Hypergeometric Parameter(s)

Hypergeometric PDF

X ~ Po(λ)

Poisson Parameter

Poisson PDF

Poisson MGF

X ~ Geo(p)

Geometric Parameter(s)

Binomial PDF

Geometric MGF

X ~ NB(r,p)

Negative Binomial Parameter(s)

Negative Binomial PDF

Negative Binomial MGF

X ~ U(a,b)

Continuous Uniform Parameter(s)

Continuous Uniform PDF

Continuous Uniform MGF

X ~ (μ,σ)

Normal Parameter(s)

Normal PDF

Normal MGF

X ~ Exp(λ) or X ~ Exp(β)

Exponential Parameter(s)

Exponential PDF

Exponential MGF

X ~ Gamma(r,λ)

Gamma Paramter(s)

Gamma PDF

Gamma MGF

X ~ Beta(a,b)

Beta Parameter(s)

Beta PDF