III. A health-food store stocks two different brands of certaintype 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 Yis
?k(x+2y) ifx≥0,y≥0,x+y≤10
f(x,y) =
Keep four decimals if necessary.
(8 pts) a. Draw the region of positive density and determine thevalue of k. (8 pts) b. Are X and Y independent? Answer by firstderiving the
marginal pdf of each variable.
(8 pts) c. Compute P (X + Y ≤ 5). (8 pts) d. Compute E(XY ).
(8 pts) e. Compute Cov(X, Y ).
