Let X1, . . . , Xn be a random sample from N(, 1). Let p = P(Xi 1) = (1 ), where is the cdf of N(0, 1). There are two estimators for p. The first one is p = (1 Xn), where we first estimate by the sample mean Xn = n 1 Pn i=1 Xi and then plug it into (1 ). The second one is p = # i n : Xi 1 n , where we compute the proportion of the samples which are less than or equal to 1. (a). Derive the limiting distribution of n(p p) as n . (b). Derive the limiting distribution of n(p p) as n