III. A health-food store stocks two different brands of certain type of grain. Let X =...

III. A health-food store stocks two different brands of 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

?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 the value of k. (8 pts) b. Are X and Y independent? Answer by first deriving 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 ).

Expert Solution

orchestra answered 1 year ago

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