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

That is, Pr(X = 1, Y = 14) = 0.02, 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 = 8.
(c) Calculate the covariance and correlation between X and Y.

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Value of Y 40 65 0.01 0.01 0.09 30 0.02 0.17 0.02 0.05 0.15 0.03 Value of X 0.02 0.10