Exam2006 - (b Find a way to test the hypothesis that μ 0 assuming that σ 2 is not known and must be estimated Explain carefully what you have

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Part B: Statistics Answer 3 of the following 4 questions. Q1 The joint probabilities of two random variables ( X and Y ) are defined by: Prob( X = x and Y = y ) = f ( x, y ). The following values are given: f(0,0) = .2, f(0,1) = .1, f(0,2) = .2, f(1,0) = .10, f(1,1) = 0, f(1,2) = α . (a) Find α . (b) Define the term marginal distribution and find all of them from the data given above. (c) Define the term conditional distribution and find all of them from the data given above. (d) Compute the conditional mean of X given that Y = 0. (e) Compute the conditional variance of X given that Y = 0. (f) Define the term ‘independence’. Are X and Y independent? Ex- plain. Q2 Suppose that X is a typical random variable from a population dis- tributed as Normal with mean= μ and variance= σ 2 . You are given the following list of realizations from a sample of size 10 drawn at random from the population: { -1.69, 3.56, 0.05, -0.41, -1.92, 2.75, 2.49, 2.95, 2.08, 3.33 } . (a) Construct a 95% confidence interval for μ assuming that you know that σ 2 = 3 Explain all of your steps.
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Unformatted text preview: (b) Find a way to test the hypothesis that μ ¿ 0 assuming that σ 2 is not known and must be estimated. Explain carefully what you have done. Q3 Suppose that X is a binomial random variable with p = . 4 and n = 50. (a) Find a way to approximate the probability that X = 22. Justify your approach. Have you used a continuity correction? Why or why not? (b) Use another approach to estimate the probability that X < 21. 1 Q4 To reduce theft, suppose that a company proposes to screen its workers with a lie-detector test that is accurate 90% of the time (for guilty subjects and for innocent subjects). The company would fire all of the workers who failed the test. Suppose that 5% of the workers steal from time to time. (a) Of the fired workers, what proportion would actually be innocent. (b) Of the remaining workers who were not fired, what proportion will still steal from time to time. 2...
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This note was uploaded on 11/20/2009 for the course ECON 5000 taught by Professor Smith during the Summer '09 term at York University.

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Exam2006 - (b Find a way to test the hypothesis that μ 0 assuming that σ 2 is not known and must be estimated Explain carefully what you have

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