A family of random variables has MGF v(t) = eat, t E R, where the value of a is a parameter defining the distribution. (a) Find the mean and variance of X as a function of a. (b) Assume X1, ..., Xn, a random sample of size n, is drawn from the distribution for a given value of a. Find the MGF, mean and variance of the sum Y = _1 Xi. (c) Let Z = Y = _ _- Xi be the sample mean of this random sample. Find the MGF, mean, and variance of Z