5. Suppose the time required for a processor to complete a set of four jobs may be modeled by a Gamma density. The average amount of time it takes is 2 hours, and the SD is 1 hour. a) Find a and 2. What is the average amount of time needed for one job? b) Set up the probability density function. c) Use several iterations of integration by parts to find an antiderivative of the density. (You may want to use the tabular method of integration by parts.) d) Using part (c), find the probability that the processor will take less than 1 hour to complete the next set of four jobs. e) Using part (c), find the probability that the processor will require more than 3 hours to complete the next set of four jobs.
5. Suppose the time required for a processor to complete a set of four jobs may be modeled by a Gamma density. The average amount of time it takes is 2 hours, and the SD is 1 hour. a) Find a and 2. What is the average amount of time needed for one job? b) Set up the probability density function. c) Use several iterations of integration by parts to find an antiderivative of the density. (You may want to use the tabular method of integration by parts.) d) Using part (c), find the probability that the processor will take less than 1 hour to complete the next set of four jobs. e) Using part (c), find the probability that the processor will require more than 3 hours to complete the next set of four jobs.
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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Transcribed Image Text:5. Suppose the time required for a processor to complete a set of four jobs may be modeled by a
Gamma density. The average amount of time it takes is 2 hours, and the SD is 1 hour.
a) Find a and 2. What is the average amount of time needed for one job?
b) Set up the probability density function.
c) Use several iterations of integration by parts to find an antiderivative of the density. (You may
want to use the tabular method of integration by parts.)
d) Using part (c), find the probability that the processor will take less than 1 hour to complete the
next set of four jobs.
e) Using part (c), find the probability that the processor will require more than 3 hours to complete
the next set of four jobs.
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