A health-food store stocks two different brands of a cer-tain type of grain. Let X 5 the amount (lb) of brand A on hand and Y 5 the amount of brand B on hand. Suppose the joint pdf of X and Y is f(x, y) = d {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?