# final20f-324.pdf - Final Examination Tuesday, December 8th,...

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Final ExaminationTuesday, December 8th, 2020MATH 3241. An experimenter wishes to compare the effectiveness of two methods oftraining industrial employees to perform an assembly operation.The se-lected employees are to be divided into two groups; the first group is trainedusing method 1 and the second group using method 2. Given that trainingan employee using method 2 costs twice as much as training using method1, 1/3 of the selected employees will be trained using method 2 and theother 2/3 using method 1. After training, each employee will perform theassembly operation, and the length of assembly time will be recorded. Anassembly is deemed to be successful if it takes less than 8 minutes. If theestimate of the difference in proportion of successful assemblies is to be cor-rect to within 5% with probability .95, how many workers must be includedin each training group?(10 marks)
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Final ExaminationTuesday, December 8th, 2020MATH 3242. Thepthquantile of a random variableYis the real numberzpthat satisfiesp=P(Yzp). Suppose thatYiiid∼ N(μ, σ2),i= 1,2,· · ·, n.(a) Find the maximum likelihood estimator (MLE) of thepthquantile of aN(μ, σ2) distribution. (Hint:StandardizeYand findzpas a functionofμ,σ2andzp, thepthquantile of aN(0,1) distribution.)
(b) Is the estimator found in part (a) consistent?Prove your claim.(Note:A simple Yes/No answer does not carry any weight.)
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Final ExaminationTuesday, December 8th, 2020MATH 3243. Suppose thatY1, Y2,· · ·, Yndenote a random sample from the Poisson dis-tribution with meanλ.(a) Findˆλ, the maximum likelihood estimator (MLE) ofλ. What is theMLE ofPλ(Y1= 0)?(5 marks)

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