The answer indicates that Var(N) = 3x0.9/(0.1x0.1) Given the proportion retained by the insurer is 0.9 shouldn't it be: Var(N) = 3x0.9^3/(0.1^2) Question attached in image.
We want E(SI) = E(N)E(Y) the N is unchanged by the proportional reinsurance - it only affects how much you pay. E(Y)= 0.9E(X)