A fair coin is independently tossed three times or until a head appears, whichever comes first. Let the random variable X denote the number of heads and let the random variable Y denote the number of tails obtained. (a) Find the probability mass function of X. (b) Find the probability mass function of Y . (c) What is the expected number of heads? (d) What is the expected number of tails? (e) What is the probability that at least two tails are observed? (f) What is the probability that exactly one head is observed?