Example Class 9

Example Class 9 - The University of Hong Kong Department of...

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Page 1 of 2 The University of Hong Kong Department of Statistics and Actuarial Science STAT1801 Probability and Statistics: Foundations of Actuarial Science (10-11) Example Class 9 1. Based on a random sample of 2 observations, consider two competing estimators of the population mean ? : 1 = 1 2 ± 1 + 1 2 ± 2 , 2 = 1 3 ± 1 + 2 3 ± 2 Which one is more efficient? 2. Let ± 1 , ± 2 ,… , ± ² be i.i.d. Bernoulli random variables such that ± ³ = 1 0 , ´ , 1 − ´ Find the maximum likelihood estimator of ´ . 3. A random sample of 5 men and 5 women had the following cholesterol levels in their blood (grams per liter): Men: 3.0 1.8 2.1 2.7 1.4 Women: 2.7 2.2 1.9 1.4 1.5 Assume the cholesterol levels are normally distributed with population mean ? µ and population variance µ 2 for men, population mean ? · and population variance · 2 for women. The two samples are assumed to be independent. a)
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This note was uploaded on 02/01/2012 for the course STAT 1801 taught by Professor Mrchung during the Fall '10 term at HKU.

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Example Class 9 - The University of Hong Kong Department of...

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