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

A health-food store stocks two different brands of a certain type of grain. Let X be the amount (in pounds) of brand A and let Y be the amount (in pounds) of brand B on hand. Suppose the joint pdf of X and Y is f(x, y) = ( Kxy, x ≥ 0, y ≥ 0, 0 ≤ x + y ≤ 10, 0, otherwise.

(a) Show that K = 1/416.6. Are X and Y independent? Why or why not?

(b) Find the marginal pdf of X and of Y .[5] [5]

(c) Show that E(X) = 4. Explain without computation why E(Y ) = 4.

(d) Using the fact that E(XY ) = 13.33 and E(X2 ) = E(Y 2 [5] ) = 20 (no need to compute these values), compute the covariance and the correlation coefficient between X and Y . Explain the correlation’ sign (positive or negative correlation).

Expert Solution

orchestra answered 2 years ago

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