Question: 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

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.

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