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The random variables $X$ and $Y$ have the joint density:

$f_{X,Y}(x,y) = \begin{cases} x + y & 0 < x,y < 1 \\ 0 & \text{otherwise}\end{cases}$

For each of the following, please provide answers as fractions, or find the answer to three decimal places:

(a) Var $(X)$

(b) Var $(Y)$

(c) Cov $(X,Y)$

(d) $\rho(X,Y)$

You can earn partial credit on this problem.