It is given that X and Y be jointly continuous random variables with joint PDF is given by:

\(f_{X,Y}(x,y)=2\ where\ 0 \leq y \leq x \leq 1\)

We have to find marginal PDF of X and Y.

\(f_{X}(x)=\int_{a}^{b}f(x,y)dy\ and\ f_{Y}(y)=\int_{a}^{b}f(x,y)dx\)

\(f_{X}(x)=\int_{0}^{1}2dy\ and\ f_{Y}(y)=\int_{0}^{1}2dx\)

\(f_{X}(x)=2\ and\ f_{Y}(y)=2\)

Thus, the marginal PDF of X and Y are:

\(f_{X}(x)=\begin{cases}2,\ 0\leq x\leq 1\\0,\ otherwise\end{cases}\)

\(f_{Y}(y)=\begin{cases}2,\ 0\leq y\leq 1\\0,\ otherwise\end{cases}\)