Question: .r *2. The joint probability function of two random variables X and Yis given in the following table: Probability Y=5 Y=6 Y=7 Y=8 X =

.r *2. The joint probability function of two random variables X and Yis given in the following table: Probability Y=5 Y=6 Y=7 Y=8 X = 1 0.01 0.18 0.24 0.06 X = 2 0.06 0.09 0.12 0.03 X = 3 0.02 0.03 0.04 0.12 a. Determine the marginal probability functions of X and Y. b. Are X and Y independent? Why or why not? c. What is the conditional probability function of X, given Y = 7'? d. What is the expected value of Y, given X = 3? e. What is the expected value of Y? of X

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