Good day In the Course Notes on page 16 there is a Question that wants us to calculate the probability of the insurer being insolvent based on the following information/assumptions: N(2) ~ Poi(60), X ~ logN(3, 1.1), c = 1200, U = 1000 Now when it comes to calculating Var[S(2)] i struggle to understand how they come up with the solution: Since S(2) = X1 + X2 + ... + XN(60). And so E[S(2)] = 60*exp{mu + 0.5*sigma^2} ( This I understand how they got here) But now how did they get to calculate Var[S(2)] = 60*exp{6 + 2.2} ? I would have thought that Var[S(2)] = 60^2*exp(6 + 1.1)*(exp(1.1) - 1)
