Let X and Z be independent random variables with X uniformly distributed on (−1, 1) and Z uniformly distributed on (0, 0.1). Let $Y = X^2 + Z$. Then X and Y are dependent.
- Find the joint pdf of X and Y.
- Find the covariance and the correlation of X and Y.
I am kind of confused about how to do this. I have been looking through my book for a similar problem or example but can not find it. I just need help with (1) the other part I can figure out pretty simply if I know the joint pdf of X and Y.
I thought of doing this but got nowhere fast $$f_X(x)=\int f_{XY}(x,y)dy$$ and trying to solve for $f_{XY}(x,y)$.