(2) Poisson distribution

P(X=x)

Conditions required for possion distribution

Events occur:

• Independently

• Singly, in space or time

• At a constant average rate (mean number in interval proportional to interval length)

Adding Poisson distributions

X~Po(λ) Y~Po(µ)

X+Y~Po(λ+µ)

E(X) and Var(X)

λ

E(X) and Var(X) of binomial distribution

E(X) = np

Var(X) = np(1-p)

When can Poisson be approximated by a binomial distribution?

When:

• n is large

• p is small

λ = np