# Thread: bivariate normal distribution transformation

1. ## bivariate normal distribution transformation

You have random variables X and Y which are Bivariate Normal. . How do you show that random variables U = X+Y and V = X-Y are bivariate normal with parameters mu1+mu2 and mu1-mu2. I took the Jacobian of the variables to get absolute value of -1/2. I substitued X= (U+V)/2 and Y=(U-V)/2 into the probability density function for the bivariate normal. The simplification of the formula has be baffled. Any assistance would be appreciated.

Fred1956

2. It would be easier to use MGFs.