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For each of these scenarios you need to clearly define WHY it is the distribution you decided, including any assumptions, and give the answer both mathematically and via RStudio (include the R code). (a) A firm buys 500 identical components, whose failure times are independent and expo- nentially distributed with mean 100 hours. (i) Determine the probability that one component will survive at least 150 hours. (ii) What is the probability that at least 125 components will survive at least 150 hours? Show all working (even if you don't perform all of the calculations, show how it would be obtained by hand). Include two methods/distributions to do this method. Compare the methods and comment on any differences • the probability distributions for both (i) and (ii); • the assumptions you made to obtain these answers and for these to be a valid distribution; • the answer to the questions (both by hand and using RStudio).

For each of these scenarios you need to clearly define WHY it is the distribution you decided, including any assumptions, and give the answer both mathematically and via RStudio (include the R code). (a) A firm buys 500 identical components, whose failure times are independent and expo- nentially distributed with mean 100 hours. (i) Determine the probability that one component will survive at least 150 hours. (ii) What is the probability that at least 125 components will survive at least 150 hours? Show all working (even if you don't perform all of the calculations, show how it would be obtained by hand). Include two methods/distributions to do this method. Compare the methods and comment on any differences • the probability distributions for both (i) and (ii); • the assumptions you made to obtain these answers and for these to be a valid distribution; • the answer to the questions (both by hand and using RStudio).

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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For each of these scenarios you need to clearly define WHY it is the distribution you decided, including any assumptions, and give the answer both mathematically and via RStudio (include the R code). (a) A firm buys 500 identical components, whose failure times are independent and expo- nentially distributed with mean 100 hours. (i) Determine the probability that one component will survive at least 150 hours. (ii) What is the probability that at least 125 components will survive at least 150 hours? Show all working (even if you don't perform all of the calculations, show how it would be obtained by hand). Include two methods/distributions to do this method. Compare the methods and comment on any differences the probability distributions for both (i) and (ii); • the assumptions you made to obtain these answers and for these to be a valid distribution; • the answer to the questions (both by hand and using RStudio).
Transcribed Image Text:For each of these scenarios you need to clearly define WHY it is the distribution you decided, including any assumptions, and give the answer both mathematically and via RStudio (include the R code). (a) A firm buys 500 identical components, whose failure times are independent and expo- nentially distributed with mean 100 hours. (i) Determine the probability that one component will survive at least 150 hours. (ii) What is the probability that at least 125 components will survive at least 150 hours? Show all working (even if you don't perform all of the calculations, show how it would be obtained by hand). Include two methods/distributions to do this method. Compare the methods and comment on any differences the probability distributions for both (i) and (ii); • the assumptions you made to obtain these answers and for these to be a valid distribution; • the answer to the questions (both by hand and using RStudio).
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(b) A certified public accountant (CPA) has found that 90% of company audits contain sub- stantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors is the third one audited? In finding this answer include: the probability distribution of Y (stating what Y is); • the assumptions you made to obtain this answer and for this to be a valid distribu- tion; • the answer to the question (both by hand and using RStudio).
Transcribed Image Text:(b) A certified public accountant (CPA) has found that 90% of company audits contain sub- stantial errors. If the CPA audits a series of company accounts, what is the probability that the first account containing substantial errors is the third one audited? In finding this answer include: the probability distribution of Y (stating what Y is); • the assumptions you made to obtain this answer and for this to be a valid distribu- tion; • the answer to the question (both by hand and using RStudio).
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