2. [12] Suppose that X1, X2, ..., Xn form a random sample from N(#, o') with unknown mean u and known variance o'. Let X = 1; (a) [3] Explain briefly, why the following quantity is a pivotal quantity for estimating A. Also, identify the distribution and parameter(\\s) of the pivotal quantity. X - H Q (b) [6] Use your pivotal quantity in part (a) to construct (find an expression for) a two-tailed (1 - @) 100% confidence interval for . [ Note: Be sure to write your confidence interval in terms of the quantiles (critical values) of the distribution in part (a).] (c) [3] Define another random variable Y which is independent of the Xy's, and that Y x ). What is the distribution and parameter( \\s) of A = V*Q? VY