400Hw05 - STAT 400 Spring 2011 Homework #5 (10 points) (due...

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STAT 400 Spring 2011 Homework #5 (10 points) (due Friday, February 25, by 3:00 p.m.) No credit will be given without supporting work. From the textbook: 2.4-18 ( ) 2.5-2 2.5-3 9.1-5 ( ) = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = NOT from the textbook: 1. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ) ! 2 ln k k , k = 1, 2, 3, … . Recall ( Homework #1 Problem 9 ): This is a valid probability distribution. a) Find μ X = E ( X ) by finding the sum of the infinite series. b) Find the moment-generating function of X, M X ( t ). c) Use M X ( t ) to find μ X = E ( X ). d) Find σ X 2 = Var ( X ).
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2. 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? 3. Mr. Statman inspects incoming large lots of thingamabobs produced by a supplier in order to determine whether to accept or reject them. In the past, incoming lots of items produced by a supplier have contained 5% defective thingamabobs 70% of the
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400Hw05 - STAT 400 Spring 2011 Homework #5 (10 points) (due...

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