Stats Distribution: Solving CW Question on Poisson Distribution

[01jbell]

hey guys/gals i have been given this cw question however i spent ages and can't seem to get my head around it can some one give me a hand

" the number N of wrecks in a particular area of sea off the Cornish coast has a poisson distribution with mean \propto . the probability that a wreck is known is p . Let X denote the number of known wrecks

(a) state the conditional distribution of X given N=n

(b) Find the Marginal Distribution of X "

thats the question now i think (a) has some hting to do with Binonial distribution

but i am complety stummped on (b)

any help would be great

thanks

 

[lanedance]

I would start by writing out the binomial distribution for
P(X=x|N=n)

the form for P(N=n) is also given

if i remember right, the joint pdf can be given to be
P(X=x, N=n) = P(X=x|N=n)P(N=n)

from that you should be able to find the marginal distribution by summing over n