Suppose that X and Y are jointly continuous with joint probability density function fX, Y px, yq " # xe´xp1`yq if x ą 0 and y ą 0, 0 otherwise. (a) Find the marginal density functions of X and Y . (b) Calculate the expectation ErXY s (c) Find the conditional density function of X given Y " y.

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.