Let X∈{0, 1} and Y∈{1, 2, 3} be two discrete random variables. Their joint probability mass function is described as P(X = 0, Y = 1) = 0.02, P(X = 0, Y = 2) = 0.16, P(X = 0, Y = 3) = 0.02, P(X = 1, Y = 1) = 0.14, P(X = 1, Y = 2) = 0.52, P(X = 1, Y = 3) = 0.14

(a) Compute and sketch the cumulative distribution function of Y.

(b) What is the value of P(Y = 2) and P(Y = 2|X = 0)?

(c) Compute E[XY], and use this result to compute the covariance of X and Y.

(d) Are X and Y independent random variables? Carefully justify your answer

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