you can prove that via the definition or the short cut formula
Use and replace X with Y.
Q: Consider and . Assume and have a bivariate normal distribution. Show that and are independent.
My work: Suppose and have a bivariate normal distribution. To show and are independent we must show .
I am having trouble with the latter computation:
How do I treat given and ?
All in all, I'm pretty stuck. Any help would be greatly appreciated.