Q_4 A sum is formed of n independent and identically-distributed (IID) random variables: T=T1+T2+\"-Tn where T; is exponentially distributed with parameter A. Under these conditions, the sum T is an Erlang random variable. (a) Using the fact that T is the sum of n independent exponential random vari- ables1 determine the mean and the variance of the Erlang random variable T. (b) The MGF of an individual exponential random variable T; is given by A /\\.5' M(s) = What is the MGF of T? (c) Use the result of (b) to compute the mean and the variance of T