Joint characteristic function

Let X and Y be two jointly distributed Gaussian random variables. E[X]=ηX , E[Y]=ηY , var(X)=σ2X , var(Y)=σ2Y , and that the correlationcoefficient between X and Y is r. What is the joint pdf of X and Y? What is the joint characteristic function of X and Y?

Let Z = aX + bY , where a,b εR

Is Z a Gaussian random variable? Why?

What is the meanand varianceof Z?

Joint characteristic functions are examines for Gaussian random variables. The mean and variance of Z are determined.