Joint density part 2

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

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

1. State the conditional distribution of \(X \mid Y\) and \(Y \mid X\)
2. Are these two random variables independent?
3. 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]