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Week+2+Problem+Set+2011 - 3 Suppose that a data-generating...

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Department of Economics Professor Dale J. Poirier University of California, Irvine October 5, 2011 ECON 123A Econometrics I Fall, 2011 Problem Set for Week 2 1. A fair coin is flipped. If it lands heads up a ball is drawn from an urn containing one red and three black balls. Otherwise, a ball is drawn from an urn containing three red and one black balls. Given that a red ball results from the experiment, what is the probability that it came from the first urn? 2. A population of voters contains 40% Republicans and 60% Democrats. It is reported that 30% of the Republicans and 70% of the Democrats favour an election issue. A person chosen at random from this population is interviewed and found to favour the issue in question. Find the probability that this person is a Democrat.
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Unformatted text preview: 3. Suppose that a data-generating process is a normal process with unknown mean : and with known variance 225. A sample of size 9 is taken from this process with the sample results: 42, 56, 68, 56, 48, 36, 45, 71, 64. Suppose your prior judgements about : can be represented by a normal distribution with mean 50 and variance 14. (a) What is your posterior distribution for : ? (b) Using your posterior distribution, find P( : > 50 * y). 4. In reporting the results of a statistical investigation, a Bayesian researcher reports that the posterior distribution for : is N(52, 10), and that a sample of size 4 with sample mean 56 was drawn from a N( : , 100) population. What were the researcher’s prior beliefs?...
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