conditional densities

Let \(X\) and \(Y\) have the following joint density:

\[ f(x,y)=\begin{cases}2x+2y -4xy & \text{for } 0 \leq x\leq 1 \ \text{and}\   0 \leq y \leq 1\\ 0& \text{otherwise}\end{cases}\]

  1. Find the marginal densities of \(X\) and \(Y\)
  2. find \(f_{Y|X}( y \,|\, X=\frac14)\)
  3. find \( \mathbf{E}(Y \,|\, X=\frac14)\)

[Pitman p426 # 2]

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