A.2. Discrete Distributions

A.2.1. Poisson

Mean = µ

Variance = µ

Parameter:

µ: mean,

A.2.2. Bernoulli

Mean = p

Variance = p(1-p)

Parameter:

p: probability of success,

A.2.3. Binomial

Mean = Np

Variance = Np(1-p)

Parameters:

N: number of trials

p: probability of success,

A.2.4. Negative Binomial

Mean = M/p

Variance = M(1-p)/p2

Parameters:

M: number of successes

p: probability of success,

Alternative Notation

Mean = µ

Variance = µ+µ-Squared/k

Parameters:

µ: arithmetic mean

k: exponent

A.2.5. Geometric

Mean = 1/p

Variance = (1-p)/p2

Parameter:

p: probability of success,

A.2.6. Hypergeometric

X = 0,1, …, N  if  N ≤ M

X = 0,1, …, M  if N > M

Mean = NM/O

Variance = N M/O (O-M)/O (O-N)/(O-1)

Parameters:

M: number of defects in sample

O: population size

N: sample size

A.2.7. Discrete Uniform

Mean = (M+N)/2

Variance = ((N-M+1)2-1)/12

Parameters:

M: lower bound

N: upper bound