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a) State the formula needed to calculate the marginal probability of P(f). b) During 200 test demands zero failures were discovered. What is the posterior probability that the software meets the business requirement?

a) State the formula needed to calculate the marginal probability of P(f). b) During 200 test demands zero failures were discovered. What is the posterior probability that the software meets the business requirement?

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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i need part a and b solution 

a) State the formula needed to calculate the marginal probability of P(f). b) During 200 test demands zero failures were discovered. What is the posterior probability that the software meets the business requirement?
Transcribed Image Text:a) State the formula needed to calculate the marginal probability of P(f). b) During 200 test demands zero failures were discovered. What is the posterior probability that the software meets the business requirement?
Question 1 A business software system is required to achieve at most 1 failure in 1000 demands (this is equivalent to a probability of failure on demand: pfd = 10-3). The business manager wants to evaluate the system before delivery using a combination of expert judgment about the process applied in its development and failure data collected during testing. From an analysis of the development process applied the business manager believes that there is a 70% chance that the system will meet the requirement and a 30% chance it is an order of magnitude worse than that (pfd = 10-2). If the pfd can take two values only, this is expressed as the prior: P(pfd = 10-3) = 0.7 P(pfd = 10-2) = 0.3 The testing process is assumed to comprise of a sequence of independent test demands, each of which can result in failure or success. The likelihood of observing f failures in d test demands is defined by the binomial distribution conditioned on the number of demands, d, and the pf d. Thus: d! P(f\d,pfd) = F!(d – f)! (pfd)' (1 – pfd)(d-r) The posterior distribution for pfd, using Bayes theorem, is: P(f]pfd,d)P(pfd) P(f) P(pfd|d, f) =
Transcribed Image Text:Question 1 A business software system is required to achieve at most 1 failure in 1000 demands (this is equivalent to a probability of failure on demand: pfd = 10-3). The business manager wants to evaluate the system before delivery using a combination of expert judgment about the process applied in its development and failure data collected during testing. From an analysis of the development process applied the business manager believes that there is a 70% chance that the system will meet the requirement and a 30% chance it is an order of magnitude worse than that (pfd = 10-2). If the pfd can take two values only, this is expressed as the prior: P(pfd = 10-3) = 0.7 P(pfd = 10-2) = 0.3 The testing process is assumed to comprise of a sequence of independent test demands, each of which can result in failure or success. The likelihood of observing f failures in d test demands is defined by the binomial distribution conditioned on the number of demands, d, and the pf d. Thus: d! P(f\d,pfd) = F!(d – f)! (pfd)' (1 – pfd)(d-r) The posterior distribution for pfd, using Bayes theorem, is: P(f]pfd,d)P(pfd) P(f) P(pfd|d, f) =
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