Answered: Airlines frequently overbook their…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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. Need help with a and e.

x	0	1	2	3	4	5
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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