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4. (10 pts) Suppose Y is a uniform random variable over [1,6]. Given that Y = y, suppose that X is a binomial random variable with parameters n = 5 and p = 1/y(a) Calculate P(X = 4) by conditioning over possible values of Y. (b) Calculate E X Y = y. (c) Calculate E X using the double expectation theorem. (d) Calculate Var(X Y = y). (e) Calculate Var(X ) using the law of total variance