c). Suppose X and Y have a joint pdf given by с 2*у, 0 < у 0, otherwise <х<1, f(x,y) Compute c, the marginal pdfs of X and Y, the conditional expectations E(YIX) and E(X|Y) d). The random vector (X, Y) has the following joint distribution 1 m Р(X 3D т, Y — п) - 11 п / 2m 15 where m 1,2,... , 5 and n 0, 1,..., m. Сompute E(Y|X). Re- mark: First derive the conditional pmf of Y given that X 1,... , 5}, and identify that the conditional pmf is a binomial pmf. т€

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Please answer all parts and round your answers to 4th decimal points. Thank you!

At bedtime, you read three books to your kids, Walker, Michael, and Luke. Together, they have 32 books. If you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.