QUESTION III Suppose an airline sells 40 tickets for a plane with only 38 seats. Suppose further that ticket holders have a probability of .9 to show up (independently). 1. What is the expected value of the number of passengers that show up at departure? (1pt) 2. What is the standard deviation of the number of passengers that show up at de- parture? (1pt) 3. What is the probability that the flight is overbooked at departure? (1pt) 4. If too many passengers show up, the airline has to pay $100 to each one that it can't accommodate on the plane. What is the expected value of the payment that the airline has to pay due to bumped passengers? (Hint: Start by defining a new random variable Y as the amount that the airline has to pay and write down the probability distribution of Y) (3pts)