An archer is given five arrows and is told to shoot at a target until he has hit the target or has used up the five arrows. The probability of a hit on each shot is 0.8, independently of the other shots. Let the number of arrows used by the archer be represented by the random variable X.
(a) Find the probability mass function of X.
(b) What is the probability that the archer has to shoot at the most two arrows before he hits the target?
(c) What is the expected number of arrows that the archer will have to shoot before he hits the target?