A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Y is the number of heads in the last three tosses.
(a) What is the joint probability mass function of X and Y?
(b) What are the marginal probability mass functions of X and K?
(c) Are the random variables X and Y independent?
(d) What are the expectations and variances of the random variables X and K?
(e) What is the covariance of X and K?
(f) If there is one head in the last three tosses, what is the conditional probability mass function of X! What are the conditional expectation and variance of X?