2. Normal Sample Mean and Sample Variance, Part 1 Let X1,X2, , X\" be i.i.d. with mean u and variance (:2. Let _ 1 n X = Xi n . r=1 denote the sample mean. In Homework 9, you constructed a random variable 1 \" _ 52 = X X 2 n _ 1 g . ) called the sample variance. Before proceeding, please review Homework 9, Question 1 in its entirety. a) For 1 g i 5 n let D1- = X,- X. Find Cou(D,-,X). b) Now assume in addition that X1, X2, , X,1 are i.i.d. normal ([1, 02). What is the joint distribution of 1?, D1, D2, , Dn_1? Explain why D\" isn't on the list. c) True or false (justify your answer): The sample mean and sample variance of an i.i.d. normal sample are independent of each other