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Get Full Access to Probability And Statistics For Engineering And The Sciences - 9 Edition - Chapter 4.4 - Problem 68
Get Full Access to Probability And Statistics For Engineering And The Sciences - 9 Edition - Chapter 4.4 - Problem 68

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# The special case of the gamma distribution in which a isa positive integer n is called ISBN: 9781305251809 122

## Solution for problem 68 Chapter 4.4

Probability and Statistics for Engineering and the Sciences | 9th Edition

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Problem 68

The special case of the gamma distribution in which a isa positive integer n is called an Erlang distribution. If wereplace b by 1/l in Expression (4.8), the Erlang pdf isf(x; l, n) 5 5l(lx)n21e2lx(n 2 1)! x \$ 00 x , 0It can be shown that if the times between successiveevents are independent, each with an exponential distributionwith parameter l, then the total time X thatelapses before all of the next n events occur has pdff(x; l, n).a. What is the expected value of X? If the time (in minutes)between arrivals of successive customers isexponentially distributed with l 5 .5, how muchtime can be expected to elapse before the tenth customerarrives?b. If customer interarrival time is exponentially distributedwith l 5 .5, what is the probability that thetenth customer (after the one who has just arrived)will arrive within the next 30 min?c. The event {X # t} occurs iff at least n events occurin the next t units of time. Use the fact that the numberof events occurring in an interval of length t hasa Poisson distribution with parameter lt to write anexpression (involving Poisson probabilities) for theErlang cdf F(t; l, n) 5 P(X # t).

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##### ISBN: 9781305251809

Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809. Since the solution to 68 from 4.4 chapter was answered, more than 271 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 88 chapters, and 2432 solutions. The full step-by-step solution to problem: 68 from chapter: 4.4 was answered by , our top Statistics solution expert on 11/08/17, 04:06AM. The answer to “The special case of the gamma distribution in which a isa positive integer n is called an Erlang distribution. If wereplace b by 1/l in Expression (4.8), the Erlang pdf isf(x; l, n) 5 5l(lx)n21e2lx(n 2 1)! x \$ 00 x , 0It can be shown that if the times between successiveevents are independent, each with an exponential distributionwith parameter l, then the total time X thatelapses before all of the next n events occur has pdff(x; l, n).a. What is the expected value of X? If the time (in minutes)between arrivals of successive customers isexponentially distributed with l 5 .5, how muchtime can be expected to elapse before the tenth customerarrives?b. If customer interarrival time is exponentially distributedwith l 5 .5, what is the probability that thetenth customer (after the one who has just arrived)will arrive within the next 30 min?c. The event {X # t} occurs iff at least n events occurin the next t units of time. Use the fact that the numberof events occurring in an interval of length t hasa Poisson distribution with parameter lt to write anexpression (involving Poisson probabilities) for theErlang cdf F(t; l, n) 5 P(X # t).” is broken down into a number of easy to follow steps, and 196 words. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9.

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