Let X X1X2X3T be a random vector with mean mx EX 123T and

Let X = [X1,X2,X3]^T be a random vector with mean mx = E(X) = [123]^T and covariance matrix a). Find the mean and covariance matrix of the random vector Y = [Y1, Y2, ]^T = AX + B , where B = [2, 1]^T and

Solution

A is of the order 2x3

X is of order 3x1

Hence Ax is 2x1 =

Ax+B = (8, 1)^T

To find mean and covariance of Y

Mean of Y = E(Ax+B) = AE(X) +B =

E(X) = (3 7/3 1)

?	C1
1	6
2	2