Solutions Questions 9-15, 9-21

Solutions Questions 9-15, 9-21 - EMSE 269 - Elements of...

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EMSE 269 - Elements of Problem Solving and Decision Making Solution by Dr. J.Rene van Dorp 1 Solution Question 9.15 a. Define: Time between two car sales Let: = Average number of Car Sales per hour 7 Assumptions meet the assumptions of the Poisson Process (Also the subscripts E and P indicate exponential distribution and Poisson Distribution in this Question) 8.5 cars per 10 hours - 0.85 cars per hour T<ÐX Ÿ>Ñ œ "/ 7†> Hence, T<ÐX#29?<=Ñœ/ œ/ œ! Þ")$ !Þ)&†# "Þ(
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EMSE 269 - Elements of Problem Solving and Decision Making Solution by Dr. J.Rene van Dorp 2 b. Define: Number of Car Sales in hours > Then: T<Ð\ œ5Ñ œ / Ð7†>Ñ 5x 7†> 5 Let: and: >œ#29?<= 5œ! Remember: 8.5 cars per 10 hours - 0.85 cars per hour It thus follows that: T<Ð\ œ !Ñ œ / œ / œ !Þ")$ Ð!Þ)&†#Ñ !x !Þ)&†# "Þ( ! Note that the results in question a and b should be the same since if the time until the first customer arrives is more than two hours it immediately follows that no customers have arrived in the first two hours and vice versa.
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Solutions Questions 9-15, 9-21 - EMSE 269 - Elements of...

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