# Math Help - Gamma-Poisson relationship.

1. ## Gamma-Poisson relationship.

If X is a gamma distribution with parameter If X is a gamma distribution with parameter 3 and λ. i.e. X~Gamma(3,λ),
then for any x,

p(X≤x)=P(Y>3),

where Y~Poisson(λx). …………(1)

(a) Verify that equation (1) is true by successive integration by parts.
(b) Express quation (1) as a probablistic relationship between Poisson process and its waiting time.

2. ## Re: Gamma-Poisson relationship.

Hey perh.

Hint: Start with the integral definition on the left and use the hints to get an integral corresponding to the right hand side. (In other words start off with P(X <= x) and integrate by parts to get P(Y > 3) = 1 - P(Y < 3).