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Problems 9 and 10 refer to the discrete random variables X and Y whose joint distribution...

Problems 9 and 10 refer to the discrete random variables X and Y whose joint distribution is given in the following table.

Y=-1

Y=0

Y=1

X=1

1/4

1/8

0   

X=2

1/16

1/16

1/8

X=3

1/16

1/16

1/4

P9: Compute the marginal distributions of X and Y, and use these to compute E(X), E(Y), Var(X), and Var(Y).

P10: Compute Cov(X, Y) and the correlation ρ for the random variables X and Y. Are X and Y independent?

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