1. Using a long rod that has length , you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be u". However, you do not know the value of u, so you decide to make n independent. measurements X1, X2, ..., Xn of the length. Assume that each X, has mean /4(unbiased measurements) and variance a. Show that X is not an unbiased estimator for #2. [Hint: For any rv Y, E(Y?) = V(Y) + [E(Y)]2. Apply this with Y = X.) b. For what value of k is the estimator X2 - kS2 unbiased for ?? Hint: Compute E(X? - k$2).1