Does anyone have any ideas on how to do this question. I've thought about it in great depth but still do not understand how to go about it. In particular, I don't understand the calculation of Pr(r big claims). Help and ideas are much appreciated.
Hiya - I'm stuck on this question too. Spent ages trying to work out what's happening and still don't even after looking at the solutions. Please help!
Quoting from the hints sheet of the ASET Let N be the number of claims and R be the number of large claims: N ~ Poisson(lambda) and R|N ~ Bin (N, p) Using Bayes Theorem: P(N-r = s|R =r) = P(R = r|N-r = s)P(N-r = s) / P(R=r) To complete the question you will need to find the distribution of R . There are two ways of doing this. Either write R as a summation of N indicator variables and find the MGF, or work from first principles and find P(R = r) by conditioning on the values of N. Does this help? If not do scream and I'll give a few more hints!
Yes the method and the Bayes Rule part makes sense, but it is finding the distribution of R that I am stuck with both of the methods that you have mentioned on how to do this (ie. by N indicator variables and by conditioning). More hints would be much appreciated. Thanks Veeko
Hi, Sorry that i have a stupid qns. In exams condition, how would you know that R|N ~ bin (1,p)? Do you assume so and state your assumptions then? Thanks alot!
R|N ~ bin (N,p) not bin(1,p) Suppose we've observed "N" claims this year. Claims are either big or small with prob. p and 1-p respectively. So it's kinda like success or failure thing. Hence, R|N ~ Bin(N, p)
