# ssrs 2012 barcode font By Theorem 11-1, the posterior density of u is beta with a 25 and b 17. in Software Printer QR Code in Software By Theorem 11-1, the posterior density of u is beta with a 25 and b 17.

By Theorem 11-1, the posterior density of u is beta with a 25 and b 17.
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11.11. A poll to predict the fate of a forthcoming referendum found that 480 out of 1000 people surveyed were in favor of the referendum. What are the chances that the referendum would be lost
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CHAPTER 11 Bayesian Methods
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Assume a vague prior distribution (uniform on [0, 1]) for the proportion u of people in the population who favor the referendum. The posterior distribution of u, given the poll result, is beta with parameters 481, 521. We need the probability that u 0.5. Computer software gives 0.90 for this probability, so we can be 90% sure that the referendum would lose.
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11.12. In the previous problem, suppose an additional 1000 people were surveyed and 530 were found to be in favor of the referendum. What can we conclude now
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We take the prior now to be beta with parameters 481 and 521. The posterior becomes beta with parameters 1011 and 991. The probability for u 0.5 is 0.33. This means there is only a 33% chance now of the referendum losing.
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Sampling from a Poisson population 11.13. The number of accidents during a six-month period at an intersection has a Poisson distribution with mean l. It is believed that l has a gamma prior density with parameters a 2 and b 5. If eight accidents were observed during the first six months of the year, find the (a) posterior density, (b) posterior mean, and (c) posterior variance.
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(a) We know from Theorem 11-2 that the posterior density is gamma with parameters nx # b>(1 nb) 5>6. (b) From (32), 4, the posterior mean 50>6 < 8.33 and (c) the posterior variance a 10 and
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250>36 < 6.94.
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11.14. The number of defects in a 1000-foot spool of yarn manufactured by a machine has a Poisson distribution with unknown mean l. The prior distribution of l is gamma with parameters a 2 and b 1. A total of 23 defects were found in a sample of 10 spools that were examined. Determine the posterior density of l.
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