A health-food store stocks two different brands of a certain type of grain. Let X
the amount (lb) of brand A on hand and Y
the amount of brand B on hand. Suppose the joint pdf of X and Y is f(x, y)
{kxy x  0, y  0, 20  x y  30 0 otherwise

a. Draw the region of positive density and determine the value of k.

b. Are X and Y independent? Answer by first deriving the marginal pdf of each variable.

c. Compute P(X Y  25).

d. What is the expected total amount of this grain on hand?

e. Compute Cov(X, Y) and Corr(X, Y).

f. What is the variance of the total amount of grain on hand?