3. (Total 10 points) Airlines often overbook flights. For a particular plane with 90 seats, 95 passengers have tickets.

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3 Total 10 Points Airlines Often Overbook Flights For A Particular Plane With 90 Seats 95 Passengers Have Tickets 1 (132.52 KiB) Viewed 46 times

3. (Total 10 points) Airlines often overbook flights. For a particular plane with 90 seats, 95 passengers have tickets. Define the random variable X as the number of ticketed passengers who actually show up for the flight. The probability mass function of X appears in the accompanying table. х 89 90 91 92 93 94 95 P(X = x) == .04 .20 .21 .19 .16 .12 .08 a. (2 points) What is the probability that the flight will accommodate all ticketed passengers who show up? b. (2 points) What is the probability that at most three passengers who actually show up could not take the flight. C. (2 points) What is the probability that not all ticketed passengers who show up can be accommodated? d. (2 points) What is the expected number of passengers who show up for the flight? e. (2 points) In the case that an airline forces a passenger off a flight for lack of space - called bumping, the passenger is entitled to $1,000 cash compensation (and of course a seat on a later flight). What is the expected amount of cash compensation payment the airline has to make? Hint: Define Y = the amount of cash compensation in each case. Then, for example, Y=0 if 90 passengers show up, Y=5000 if 95 passengers show up, etc. What are all possible values of Y? Write down the probability distribution of Y and use it to find E(Y).