Question: If the joint density of \(X\) and \(Y\) is given by

\[f(x,y)=\left\{ \begin{aligned} & \frac{1}{4}\left( 2x+y \right)\text{ for }0<x<1,\text{ }0<y<2 \\ & \text{ }0\text{ for elsewhere} \\ \end{aligned} \right.\]

(a) Find the marginal distribution function of \(X\).

(b) Find the marginal distribution of \(Y\).

(c) Find the conditional density function given \(X=\frac{1}{4}\)