STAT 424 Homework 2 Due February 21, 4PM 20 pts for each problem below (in total, 100pts): 1. Let X = (X1, X2, X3)? be a random vector with zero mean...

I'm having trouble with parts (a) and (c) of question 1. In our textbook, the examples always include a response variable and other examples I've found online also have a response variable and are only linear functions of one X. I understand the theory behind best linear estimators as well as the Gauss-Markov theorem and BLUE, would any of these apply to linear predictors?

For (c) I know I need (a), and I know the multiple correlation coefficient equation, but I'm not sure how to calculate

STAT 424 Homework 2Due February 21, 4PM20 pts for each problem below (in total, 100pts):1. Let X = (X1, X2, X3)? be a random vector with zero mean and covariance matrixE(a). Find the best linear prediction X1 of X1 as a linear function of X2 and X3;(b). The multiple correlation coefficient of X1 with the random vector (X2, X3) ? isR =(Var(X1)) 1/2ShowR= (1 _ Var(X1 - X 1) ) 1/2Var(X1)(c). Find Var(X1 - X1) and the multiple correlation coefficient R.tribution2. Let (X1, Y1), ..., (Xn, Yn) be independent samples from the bivariate normal dis-For fixed d E R, find constants K, m, 0 such thatT= K-X -Y - S[X, -Y) - (x -nfollows a noncentral t-distribution tm(0) with degrees of freedom m and noncentralparameter 0.