INFERENCE STATISTICS

QUESTION 3 Suppose that X1, X2, ..., X\" is a random sample from an exponential distribution with mean [3. (a) Show that 3:" is a consistent estimator of ,8. (4) (b) Determine the Cramer-Rao lower bound of the variance of an unbiased estimator of f]. (7) (c) Prove or disprove that Y is a minimum variance unbiased estimator of f}. (3) (d) Write down the expression of an approximate 95% condence interval for ,6 when n is large. (3)