Problem 7. A joint PDF on a triangular region This figure below describes the joint PDF of the random variables X and Y. These random variables take values in [0, 2] and [0, 1], respectively. At a = 1, the value of the joint PDF is 1/2. 0.8 fxy (x, y) = 1 fx.y (z, y) = 0.6 04 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 1. Are X and Y independent? Yes )No 2. Find fx (). Express your answers in terms of , using the standard notation. If 0 > 2: fx (z) = X 3. Find frix (y | 0.5). If 0 1/2: frix (y | 0.5) = x 4. Find fxy (2: | 0.5). If 1/2 > 3/2: fxx (z | 0.5) = X 5. Let R = XY and let A be the event that { X