Suppose that

SN=X1+X2++XN=Xi,

where{Xi, i= 1, , N}are independent and identically distributed ran- dom variables andNis a non-negative random variable independent ofXis. Letand2be the mean and variance ofXis, respectively (i.e.E(Xi) =andV(Xi) =2for alli= 1,,N).

N SN = X1+ X2+ . . . + XN => Xi, i=1 where {Xi, i = 1, . .., N} are independent and identically distributed ran- dom variables and N is a non-negative random variable independent of Xis. Let u and of be the mean and variance of Xis, respectively (i.e. E(Xi) = u and V(Xi) = 02 for all i = 1, ..., N). Find E(SN) and V(SN). [Hint: Use the fact that E(SN) = E[E(SN|N)] and V(SN) = EV (SN|N)] + VIE(SNIN)]]