Problem 19. Consider three sample variances, S?, S, and $3. Suppose that the sample vari- ances are comprised of n1, 12 and n3 iid draws from normal populations N(/41, 62), N(12, 02) and N(/43, 02), respectively. Argue that (n1 - 1)$3 + (n2 - 1)$3 + (n3 - 1)$3 n1 + n2 + n3 - 3 is an unbiased estimate of o2