5-2. Let a random experiment consist of tossing a fair coin twice. Define the random variable X to be the number of heads obtained in the two tosses and let the random variable Y be the opposite face outcome. Determine the points within the sample space S and the values of X and Y on S. Next, specify the bivariate probability distribution between X and Y. Find:

(a) P(X = 2|Y = 1)

(b) The marginal distribution of Y

(c) The conditional distribution of X given Y = 0. Are X and Y independent?