7. Airlines routinely overbook flights based on the expectation that some fraction of booked passengers will not show up for each flight. For a particular flight, there are only 50 seats, but the airline has sold 52 tickets. Assume that a booked passenger will not show for the flight with probability 5 (a) Let X be the number of passengers that arrive for the flight. Under what assumption (s) is X a Binomial random variable? (b) Find the exact probability that 51 passengers arrive. (c) Find the expected number and variance of the number of passengers that arrive for the flight