Question: 2.9 X and Y are discrete random variables with the following joint distribution: That is, Pr(X = 3, Y = 2) = 0.04, and so

2.9 X and Y are discrete random variables with the following joint distribution:

Value of Y 2 4 6 8 10 3 0.04 0.09 0.03

That is, Pr(X = 3, Y = 2) = 0.04, and so forth.

a. Calculate the probability distribution, mean, and variance of Y.

b. Calculate the probability distribution, mean, and variance of Y given X = 6.

c. Calculate the covariance and correlation between X and Y.

Value of Y 2 4 6 8 10 3 0.04 0.09 0.03 0.12 0.01 Value of X 6 0.10 0.06 0.15 0.03 0.02 9 0.13 0.11 0.04 0.06 0.01

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