Suppose we have a vector z which has a multivariate normal distribution, Let y = a′z for some k × 1 vector a, and let x = Bz for some p × k matrix B. Using (A.17) and (A.18) in Appendix A.7, show...

Suppose we have a vector z which has a multivariate normal distribution,

Let y = a′z for some k × 1 vector a, and let x = Bz for some p × k matrix B. Using (A.17) and (A.18) in Appendix A.7, show that the conditional distribution of y|x is normal and that the conditional mean is a linear function of x. Get expressions for the parameters of the conditional distribution.