Q3. Suppose you roll two fair dice. A random variable X is the sum of the two fair dice and a random variable Y is the minimum of the two fair dice.
(a) Are X and Y independent?
(b) Write down the elements in the joint sample space X x Y and give their probabilities.
(c) Calculate P(X ≥ 8|Y = 3).
(d) Calculate P(Y=3|X ≥ 28).