(a) Let Y(l) be the first order statistic of a random sample of size n from a distri- 0 < y < 00, zero elsewhere. What is the bution that has pdf f (y) limiting distribution of Zn 0)? (b) (i) Suppose Xn is the sample mean of a random sample of size n from a pdf f (x) distribution that has a Gamma(2, 1/2) (where a 2, {3 0 < x < 00, zero elsewhere. Use the Central Limit Theorem to deduce that the random variables vfi(Xn 1) converges in distribution to N(o, 1/2). (ii) Use the Delta method to find the limiting distribution of the random vari- ables xn- 1). (iii) Use the limiting distribution of part (ii) to find an approximate probability for X36 1.15).