A group insurance includes TWO policies. Annual claim frequency, N, is assumed to have a common

binomial distribution, so if the claim rate, q were known, then

(N|Q = q) Bin [2, q]

and the prior distribution of Q is

P [Q = 0.2] = P [Q = 0.6] = 0.5.

(i) Determine E [N]

(ii) Evaluate P [N = 0]

(iii) Derive P [N = 2]