Airlines frequently overbook their flights. Suppose that for Flight 23 to Miami from New York there are always between 0 and 5 passengers who cannot be accommodated because of overbooking. Let x be the number of passengers who cannot be accommodated and suppose x has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution. 1 2 3 p(x) .35 .20 .18 .15 .10 .02 F(x) .35 .55 .73 b .98 1 a. What is the probability that all passengers can be accommodated? b. If F is the cumulative distribution function of x, then what is the value of b? c. What is the expected value of x? d. Calculate the expected value of x2 e. Calculate the expected value of (x - 1.51)² f. What is the probability that all passengers can be accommodated on all 5 days of a workweek? (Assume independence between days.) g. Assuming independence of passenger count between days, what is the probability that the maximum number of non- accommodated passengers during a 5 day workweek is less than or equal to 1? h. Assume the airline must pay a delay fee of $197 to each non-accommodated passenger. What is the expected total delay fee the airline pays on a single day?

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