If X and Y have a bivariate normal distribution with correlation p, show that X +Y is normally distributed
This seems like a pretty standard proof but cant find it anywhere. Simply adding the marginal distributions, X+Y is what I tried but how is the correlation coefficient introduced?
I then looked at convolution but that didnt seem to go the right way either...
Thanks for your reply.
How do we handle the standard deviations of x and y when converting to U and V? Additionally, taking this approach means we start from the marginal distributions of X and Y. Isnt there a way to start from the joint bivariate distribution of X and Y since this includes the correlation term?