Hw3_solution - HomeworkSolutions#3 Q3 Supplemental...

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CEE 304  -  Uncertainty Analysis in Engineering Homework Solutions #3 Q3. Supplemental exercise (p.127) # 103 (Devore 6 th edition– p141, #99) a) Supplemental exercise (p.141 # 99): if p = 0.1 and n = 3, what is the expected number of tests using this procedure? What is the expected number when n = 5? b) NOTE: If one just tested everyone's blood, this requires n tests (n = 3 or 5). As a result the average number of tests per individual would be 1.00. For your answers in a), what was the average # of tests per individual? c) Can you find an equation whose solution is the best value of n? Solution is an equation that needs to be solved numerically for root. HINT: A total population is of size N, can be broken into subgroups of size n, and a test performed on each of the N/n subgroups to see if anyone in that group has the disease! So how do we find the optimal n? Answer: (a) For p = 0.1, what is the expected number of tests? E[X] p = probability an individual has the disease n = # of individuals independently selected for testing X = # of tests conducted
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