QUESTION 3 (a) Consider the shifted exponential distribution with probability density function given by fx (x; 0) = le-1(x-0), x20. When 0 = 0, this density reduces to the usual exponential distribution. When 0 > 0, there is only positive probability to the right of 0. Find the maximum likelihood estimator of 1 and 0, based on a random sample of size n. (10) (b) Let X1, X2 and X3 be independent random variables such that E (X1) = 01; E (X2) = 02; E(X3) = 01+02; Var (X1) = Var (X2) = Var (X3) = 62. Determine the least squares estimators of 01 and 02