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A random number N of jobs are to be processed one at a time on a single processor. The processing time of the ith job is exponentially distributed with parameter 1, independent of the other processing times and N. The number of jobs N has a geometric distribution with parameter 1/2. What is the expected value of the total processing time? What is the probability that the total sum of processing times is greater than 2?

A random number N of jobs are to be processed one at a time on a single processor. The processing time of the ith job is exponentially distributed with parameter 1, independent of the other processing times and N. The number of jobs N has a geometric distribution with parameter 1/2. What is the expected value of the total processing time? What is the probability that the total sum of processing times is greater than 2?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A random number N of jobs are to be processed one at a time on a single processor. The processing time of the ith job is exponentially distributed with parameter 1, independent of the other processing times and N. The number of jobs N has a geometric distribution with parameter 1/2. What is the expected value of the total processing time? What is the probability that the total sum of processing times is greater than 2?
Transcribed Image Text:A random number N of jobs are to be processed one at a time on a single processor. The processing time of the ith job is exponentially distributed with parameter 1, independent of the other processing times and N. The number of jobs N has a geometric distribution with parameter 1/2. What is the expected value of the total processing time? What is the probability that the total sum of processing times is greater than 2?
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