Hi there, I need help to solve that problem.
Suppose that the conditional distribution of N, given that Y = y, is Poisson with mean y. Further suppose that Y is a gamma random variable with parameters (r, λ), where r is a positive integer.
(a) Find E[N].
(b) Find Var(N).
(c) Find P(N = n)
My work so far.
a) E(N)=E(E(N|Y)=E(Y)=rλ
b)Var(N)=E(Var(N|Y))+Var(E(N|Y))=E(Y)+Var(Y)=rλ+rλ ^2
Is my work correct so far, and also I am not sure how to start part c.
Thanks for your help!
Suppose that the conditional distribution of N, given that Y = y, is Poisson with mean y. Further suppose that Y is a gamma random variable with parameters (r, λ), where r is a positive integer.
(a) Find E[N].
(b) Find Var(N).
(c) Find P(N = n)
My work so far.
a) E(N)=E(E(N|Y)=E(Y)=rλ
b)Var(N)=E(Var(N|Y))+Var(E(N|Y))=E(Y)+Var(Y)=rλ+rλ ^2
Is my work correct so far, and also I am not sure how to start part c.
Thanks for your help!
Need help with that problem
