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.