Homework9 - 1.230 0.490 1.080 0.590 0.280 1.200 0.710 0.190...

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Homework 9 Due Date: 11/29/2010, but you are welcome to submit it next Wednesday. Problem #1: Suppose that the current measured in a thin copper wire follows a uniform distribution with a range of [ ] θ , 0 and the probability density function ( 29 = elsewhere x x f 0 0 / 1 A sample of five measurements is taken and the data are shown below (in milliamperes): 11.5, 3.2, 7.3, 19.2, 16.7 Show that the maximum likelihood estimate of is 2 . 19 max = = x . Problem #2: Assume that the mercury contamination in a largemouth bass follow a normal distribution with unknown mean µ (ppm), but a known standard deviation σ =0.35 (ppm). A sample of ten fish was selected from Florida lakes and mercury concentration in the muscle tissue was measured (ppm).
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Unformatted text preview: 1.230 0.490 1.080 0.590 0.280 1.200 0.710 0.190 0.730 0.340 (a) Find the maximum likelihood estimate of the unknown population mean µ . Note: You are expected to write down the likelihood function and log-likelihood function and maximize the log-likelihood function with respect to µ . (b) Construct a 95% confidence interval for µ . (c) How large a sample is required if we want to be 95% confident that our estimate of µ is off by less than 0.05 ppm. Problem #3: 9.12 (Here 2.45 is the sample standard deviation): (10.15, 12.45). Problem #4: 9.25 (Prediction interval): (6.05, 16.55). Practice problem: Not required for anyone. 9.4 and 9.8...
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Homework9 - 1.230 0.490 1.080 0.590 0.280 1.200 0.710 0.190...

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