Let (X,Y) be continuous random variables with joint PDF:

(,)={2 if0 x 1 and0 y 1

0 else

Part a)

Solve for c.

Part b)

Find the marginal distributions fX(x) and fY(y).

Part c)

Solve for E[X] and E[Y].

Part d)

Using the joint PDF, solve for E[XY].

Part e)

Are X and Y independent?