B1. Suppose we have X1, X2, X, which are i.i.d. and come from the uniform distribution ... Uniform(n,+ n), n>0; 0 = (,7) (a) Use the Method of Moments to estimate and n. (b) Determine whether the estimate derived by the Method of Moments is biased for . (c) Use the Maximum Likelihood method to estimate and n. Use the notation: X(1) = min(X1, X2, Xn) and X(n) = max(X1, X2,..., Xn) (d) It can be derived that n-l 1x (4)-(1-2-(-1)). fx) (x)= n n-1 21 x = [p = n, p+n] 1x(x)-((-1))" = Determine whether the estimate obtained by the Method of Maximum Likelihood is biased for . Hint: Use substitutions y=1-(-) and (-) 2 (e) Describe the criteria which can be used to choose between these two estimates.