# Consider the generalization of the ordinary Poisson process, called the com-pound ## Problem 5 Chapter 6.4

Probability and Statistics with Reliability, Queuing, and Computer Science Applications | 2nd Edition

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Problem 5

Consider the generalization of the ordinary Poisson process, called the com-pound Poisson process. In an ordinary Poisson process, we assumed that theprobability of occurrence of multiple events in a small interval is negligible withrespect to the length of the interval. If the arrival of a message in a LAN (localarea network) is being modeled, the counting process may represent the num-ber of bytes (or packets) in a message. In this case suppose that the pmf of thenumber of bytes in a message is specified:P[number of bytes in a message = k] = ak, k 1.Further assume that the message-arrivals form an ordinary Poisson process withrate . Then the process {X(t) | t 0}, where X(t) = number of bytes arriving inthe interval (0, t], is a compound Poisson process. Show that generating functionof X(t) is given byGX(t)(z) = et[GA(z)1],whereGA(z) = k1akzk.

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Statistics: Intro information  Data: What is it o information we collect and organize o facts and figures o numbers and text  What is the point of Statistics o To process data so that it is useful o Provide meaningful information in an easily accessible way o Answer questions o Tell...

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##### ISBN: 9781119285427

Probability and Statistics with Reliability, Queuing, and Computer Science Applications was written by Patricia and is associated to the ISBN: 9781119285427. This textbook survival guide was created for the textbook: Probability and Statistics with Reliability, Queuing, and Computer Science Applications , edition: 2. This full solution covers the following key subjects: . This expansive textbook survival guide covers 81 chapters, and 351 solutions. The answer to “Consider the generalization of the ordinary Poisson process, called the com-pound Poisson process. In an ordinary Poisson process, we assumed that theprobability of occurrence of multiple events in a small interval is negligible withrespect to the length of the interval. If the arrival of a message in a LAN (localarea network) is being modeled, the counting process may represent the num-ber of bytes (or packets) in a message. In this case suppose that the pmf of thenumber of bytes in a message is specified:P[number of bytes in a message = k] = ak, k 1.Further assume that the message-arrivals form an ordinary Poisson process withrate . Then the process {X(t) | t 0}, where X(t) = number of bytes arriving inthe interval (0, t], is a compound Poisson process. Show that generating functionof X(t) is given byGX(t)(z) = et[GA(z)1],whereGA(z) = k1akzk.” is broken down into a number of easy to follow steps, and 141 words. The full step-by-step solution to problem: 5 from chapter: 6.4 was answered by Patricia, our top Statistics solution expert on 03/05/18, 07:23PM. Since the solution to 5 from 6.4 chapter was answered, more than 219 students have viewed the full step-by-step answer.

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