Question

Suppose that X and Y are bivariate normal with density quadratic term Ξ 1 (a-2 px yty xor f(x,y) = This means that X and Y are correlated standard normal random variables since We will show that X and the new random variable Z defined as Since Z is obtained as a linear combination of normal random variables, it is also a. What is the mean of Z, call it E[Z]? b. What is the variance-covariance matrix of the random vector (X,Y) are independent, standard normal. (Intuitively we are "subtracting off" from Y the "stuff" in the X direction). Relax a little, we'll try to walk you through this problem. say xr Find the variance covariance matrix of (X,Z) , call it result that, if we already know the variance-covariance matrix of (X, Y) then we can express the variance covariance matrix of (X,Z) as c. х.z. by using the First note that this this is a linear transformation with 0 X.2 d. By reference to your matrix ΣΧ.Z justify that X and Z are independent, and standard normal. To unpack how the original Xand Y are distributed, recall the formula for a bivariate normal random vector End of documentI guadratle term

Answer 1