Exercise 1.1. The Central Limit Theorem tells us that the estimator in is asymp- totically normal. In particular, we can construct the following random variable, Yn, such that ~+N(0,1), where NW, 02) is a normal random variable with mean u and variance a2. Explain why the estimator X n behaves roughly like N (p, %) . [HINT: First, note that Yn is approximately N(0, 1). Now, reformulate the given equation to express X n as a function of Y\"; what kind 2f function do you gt? Combine these two facts to determine the distribution of X n by computing E(Xn) and Var(fn).]