Problem 2 Let U1, U2, . . . , U" be a sample consisting of independent and identically distributed normal random variables with expectation zero and unknown variance 02. 1 pt (a) If we let V = 2L1 U3, what is the distn'bution of the pivotal quantity 1/702? 3 pts (b) Using the central limit theorem, give an approximate value of the 5th and 95th percentiles of the distribution of V/o51 for large n. Zpts (c) Hence, give a simple expression for an approximate 90% condence interval for 02 in terms of the sample size n (assumed to be large) and the observed values u1,u2, . . . , u" of the sample. (Do not use any symbols for unknown quantiles; instead use the approximate values of those quantiles obtained in (b))