Here's the problem:
A Flight has 20 seats and enough demand to sell out all flights (not enough to justify buying bigger plane). All seats sell for $200.
Probability a passenger with reservation shows up = p. The probability of “No show”=1-p. The occurrence of “Show/No show” is independent among passengers. Passengers who are turned away due to “overbooking” are given $240 (the purchase price plus a 20% penalty to airline) The number of reservations made for each flight is chosen by airline (not random): n
The number of booked passengers who show up is a random variable: X
- What is the probability distribution of X?
- Write out the Revenues to the airline for a flight as a function of X
- Write out the expected Revenues to the airline
- What is the effect of increasing n on expected revenues for a given p?
- What is the effect of increasing p on expected revenues for a given n?
- When would it make no sense to overbook flights?
My thoughts: I think the answer to the first part is that it is a binomial distribution (since we have two distinct outcomes and a constant and independent probability of success). However, I am facing problem in the remaining parts. Can someone please explain it to me? Thanks so much :)