Let \(X\) and \(Y\) have joint density

\(f(x,y) = 90(y-x)^8, \quad 0<x<y<1\)

- State the conditional distribution of \(X \mid Y\) and \(Y \mid X\)
- Are these two random variables independent?
- What is \( \mathbf{P}(Y \mid X=.2 ) \) and \( \mathbf{E}(Y \mid X=.2) \) ?

What is \( \mathbf{P}(Y \mid X=.2 ) \) and \( \mathbf{E}(Y \mid X=.2) \)

[Adapted from Pitman pg 354]