Poisson Distribution

Poisson Distribution

a discrete probability distribution

expresses the probability of a given number of events occurring in a fixed interval of time/space

Constraints

events must:

• occur with a constant rate

• occur at a single rate

• be independent of each other

λ

the average number of times that the event will occur in a single interval

X ~ Po(λ)

Adding Poisson Distributions

if X ~ Po(λ) and Y ~ Po(μ) then

X + Y ~ Po(λ + μ)

Using Poisson to Approximate Binomial Distribution

if X ~ B(n,p)

• n is large

• p is small

• then X can be approximated by Po(λ) where λ ≈ np

usually np will be <= 10

Hypothesis Testing for the Mean

there is also a table in the formula book to help you with this

Critical Regions

one tailed test = 1

two tailed test = 2