So I have X1 and X2 are iid standard normal. Then I have Y=X1^2+ X2^2 and Z=X1/(X1^2+x2^2) I'm supposed to find the distribution of Y and Z and then determine if they are independent. Clearly Y is chi squared with degrees of freedom 2. But I have no idea how to find the distribution of Z. I know there is a shortcut without using the jacobian, like I did with the Chi Squares, but I'm not sure how to do it. I know Y and Z are not independent because with some algebra, Y=Y*Z^(2)+X2 So Y depends on Z and vice versa, therefore they cannot be independent. Is that true?