# 409Hw14 - STAT 409 Homework#14 Fall 2009(due Wednesday...

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Homework #14 Fall 2009 (due Wednesday, December 9, by 4:30 p.m.) 1. When correctly adjusted, a machine that makes widgets operates with a 5% defective rate. However, there is a 10% chance that a disgruntled employee kicks the machine, in which case the defective rate jumps up to 30%. a) Suppose that a widget made by this machine is selected at random and is found to be defective. What is the probability that the machine had been kicked? b) A random sample of 20 widgets was examined, 4 widgets out of these 20 are found to be defective. What is the probability that the machine had been kicked? 2. 7.2-1 3. Consider a random sample X 1 , X 2 , … , X n from a distribution with p.d.f. f ( x ; λ ) = λ x λ – 1 , 0 < x < 1, zero elsewhere, λ > 0. a) Find the maximum likelihood estimator of λ , λ ˆ . b) Let λ have a prior p.d.f. which is gamma with parameters α and θ . Find the conditional mean of λ given X 1 = x 1 , X 2 = x 2 , … , X n = x n . Show that it is a weighted average of the maximum likelihood estimator

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## This note was uploaded on 10/12/2011 for the course STATISTICS stat 410 taught by Professor Stepanov during the Spring '11 term at University of Illinois, Urbana Champaign.

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409Hw14 - STAT 409 Homework#14 Fall 2009(due Wednesday...

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