roblem 3. Consider the following joint probability mass function of two random variables X = {c, d] and Y € {1,2,3}: PxY(2,3) 1 2 3 0.1 0.3 0.2 0.2 0.1 0.1 C d Here c and d are some real numbers. 1. Is this a valid joint pmf? Provide formal justification. Compute Pr(X= c). Compute Pr(Y = 3). 2. Compute the conditional pmf of Y given X = c, i.e., compute Pr(Y=y|X = c) = py|x (ylc), for y = 1,2,3. Comp the expected value of this conditional pmf. 3. Compute the conditional pmf of X given Y = 3, i.e., compute Pr(X = x|Y = 3) = pxy (x|3), for x = c, d. Comp the expected value of this conditional pmf.

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