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HW 5 Solutions - Steven Weber Dept of ECE Drexel University...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2010) Homework 5 Solutions Question 1: Exercise 12, § 3.2, p.98 Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying table: y 45 46 47 48 49 50 51 52 53 54 55 p ( y ) 0 . 05 0 . 10 0 . 12 0 . 14 0 . 25 0 . 17 0 . 06 0 . 05 0 . 03 0 . 02 0 . 01 (1) What is the probability that the flight will accommodate all ticketed passengers who show up? P ( Y 50) = p (45) + · · · + p (50) = 0 . 83 . (2) What is the probability that not all ticketed passengers who show up can be accommodated? P ( Y > 50) = 1 - P ( Y 50) = 0 . 17 . (3) If you are the first person on the standby list, what is the probability that you will be able to take the flight? What is this probability if you are the third person on the standby list? P ( Y 49) = p (45) + · · · + p (49) = 0 . 66 , P ( Y 47) = p (45) + · · · + p (47) = 0 . 27 . (4) Question 2: Exercise 13, § 3.2, p.98 A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a given time. Suppose the pmf of X is as given in the accompanying table.
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