Question: Suppose that

\[{{f}_{Y|X}}\left( y|x \right)=\left\{ \begin{aligned} & 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<y<x+1 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right.\]

and X has a Uniform (0,1) distribution

(a) Find \(E\left( Y \right)\)

(b) Find \({{f}_{X|Y}}\left( x|y \right)\)

(c) Find \(\Pr \left( X+Y<1 \right)\)