CT6 Sept 2007 Q3

Could Someone Explain Q No 3 Of Sept 2007

 

Hi

The thread is no longer available. Can someone help with an explanation for this question?

 

The easiest way to do this is I think to use Bayes Theorem.
N is Poisson(lambda), and R|N is binomial(N,p).
So, using Bayes Theorem:
P(N-r = s | R = r) = {P(R = r| N-r = s) P(N-r = s)} / P(R=r)
The conditional probability is binomial. The second probability is Poisson. The probability in the denominator is obtained as:
Summation {P(R = r| N=n) P(N = n)}

Michael Hosking