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,
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.