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A group insurance includes TWO policies

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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) Find P [N2= 0 |N1= 0]

(ii) Evaluate E [N2|N1= 0]