Problem 7 (Independence and Correlation) X1, X2 are i.i.d. random variables with uniform distribution over [0, 1], and we define U = max(X1, X2) and V = min (X1, X2). a. Find the mean of U and V, then compare the variances of U and V. b. Find the joint p.d.f. of (U, V). Are they independent? c. Find the correlation coefficient of U and V, p(U, V). We recall that P(U, V) = COU(U, V) OUOV d. X1, X2, ..., Xn are i.i.d. random variables with uniform distribution over [0, 1]. Let U = max(X1, X2, . . ., Xn) and V = min(X1, X2, ..., Xn). Now assume n is growing larger and larger. How does the correlation coefficient of U and V behave? Find the limit