Question: Assume that \(\left( X,Y \right)\) is a two-dimensional continuous random variable with pdf

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

a) Find the marginal densities for X and Y.

b) Compute the probability \(\Pr \left( X\le 0.6 \right)\). Find \(E\left( X \right)\)

c) Find the conditional density of X given that Y takes on the value y = 1/2.