Question 3.7 (6 marks) A fair coin is flipped 3 times and the results are recorded. Let X and Y be random variables such that X is the total number of times heads is obtained and Y is the number of times heads is obtained in the first two flips. (Remember flipping a fair coin is equivalent to selecting an element of { heads, tails } uniformly at ran- dom.) a) What is Pr( X is even)? b) Are the events "X is even" and "Y = 0" independent? Explain. c) Are X and Y independent random variables? Explain. d) Let Z be the random variable with probability distribution given as follows. Pr( Z = =) Find E[Z] and Var[Z]