Poisson Distributions

Question 1

Poisson distribution formula, X~Po(λ)

Answer 1

Question 2

In order for the Poisson distribution top be a good model, the events must occur:

Answer 2

• independently
• singularly, in space or time
• at a constant average rate (proportional to the length of the interval)

Question 3

If two Poisson variables X and Y are independant, the variable Z = X + Y also has a Poisson distribution.

Answer 3

And Z = X + Y

Question 4

Mean of Poisson distribution, X~Po(λ)

Answer 4

Question 5

Variance of the Poisson distribution

Answer 5

Question 6

Mean of a binomial distribution, X~B(n,p)

Answer 6

Question 7

Variance of a binomial distribution, X~B(n,p)

Answer 7

Question 8

Binomial distribution can be approximated by the Poisson distribution when

Answer 8

• n is large
• p is small
  Where λ = np