Question 1. X and Y are discrete random variables with the following joint distribution: Value of Y 14 22 30 40 65 1 0.02 0.05 0.10 0.03 0.01 0.17 0.15 0.05 0.02 0.01 5 8 0.02 0.03 0.15 0.10 0.09 Value of X That is, P(X= 1, Y = 14) = 0.02, and so forth. (1) Calculate the probability distribution, mean, and variance of Y. (2) Calculate the probability distribution, mean, and variance of Y given X = 8. (3) Calculate the covariance and correlation between X and Y.

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