Let X1 X2 Xn be a sequence of n independent and identically

Let X_1, X_2,... X_n be a sequence of n independent and identically distributed exponential random variables with parameter A. Let S_n = X_1 + X_2 + ... + X_n. Determine E[S_n] and Var(S_n). Let M_n = (X_1 + X_2 +...+ X_n)/n. Determine E[M_n] and Var(M_n). Let Z_n = (S_n - E[S_n]) / sqrt Var(S_n). Determine E[Z_n] and Var(Zn).

Solution