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#1




SOA #181
I am getting the correct E[S] and Var(S):
E[S] = lamda * theta Var(S) = 2 * lamda * theta^2 However, I don't understand why v = 4 and a = 3. I am getting v = 2 and a = 1, which is apparently a trap. I am getting: v = E[2 * lamda * theta^2] = 2*1*1 = 2 a = Var(lamda * theta) = 1*1 = 1 Help please! 
#2




What are the distributions for lambda and theta? One mistake is the variance of a product isn't the product of variances even if the RVs are independent.

#3




Quote:
remember 1. E[theta^2]=2 since theta is Possion, Var[theta]+E[theta]^2 = 1 + 1^2 therefore E[2 * lamda * theta^2] = 2 * 1 * 2 = 4 2. Var[lambda *theta]=E [lamba^2]*E[theta^2]  E[theta]^2 * E[lambda]^2 = 2*2 1*1
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