Given the gaussian random vector x in problem 571 y ax b

Question

Given the Gaussian random vector X in Problem 5.7.1, Y = AX + b, where

And b = [-4 -4 -4]' Calculate

(a) the expected value µ_Y,

(b) the covariance C_Y,

(c) the correlation R_Y,

(d) the probability that -1 ≤ Y2 ≤ 1

Problem 5.7.1

X is the 3-dimensional Gaussian random vector with expected value µX = [4 8 6]' and covariance

Calculate

(a) the correlation matrix, R_X,

(b) the PDF of the first two components of X, fX₁,X₂ (x₁, x₂),

(c) the probability that X1 > 8