Let x denote a p-variate random vector. Let x denote the population mean vector, and x denote the population covariance matrix of x.

Assume that x and x exist as finite quantities. Let y=Ax+b where A is a nonsingular matrix. Let y denote the population mean vector, and y

denote the population covariance of y. Show that y=Ax+b and that y=AxAT .