Introduction to Probability and Statistics for Engineers and Scientists
264 Chapter 7: Parameter Estimation approximately .05 would require an approximate sample of size n= 4(z.005)^2 (.05)^2 26 30 ( ...
*7.6Confidence Interval of the Mean of the Exponential Distribution 265 *7.6Confidence Interval of the Mean of the Exponential D ...
266 Chapter 7: Parameter Estimation SOLUTION From Program 5.8.1b (or Table A2), we see that χ.025,20^2 =34.169, χ.975,20^2 =9.66 ...
*7.7Evaluating a Point Estimator 267 Definition Letd=d(X) be an estimator of the parameterθ. Then bθ(d)=E[d(X)]−θ is called theb ...
268 Chapter 7: Parameter Estimation EXAMPLE 7.7b Combining Independent Unbiased Estimators. Letd 1 andd 2 denote inde- pendent u ...
*7.7Evaluating a Point Estimator 269 to the conservation organization, then they should estimate the acidity of the sampled wate ...
270 Chapter 7: Parameter Estimation EXAMPLE 7.7c LetX 1 ,...,Xndenote a sample from a uniform (0,θ) distribution, where θis assu ...
*7.7Evaluating a Point Estimator 271 Therefore, E[d 2 ]= ∫θ 0 x nxn−^1 θn dx= n n+ 1 θ (7.7.1) Also E[d 22 ]= ∫θ 0 x^2 nxn−^1 θn ...
272 Chapter 7: Parameter Estimation To determine the constantcresulting in minimal mean square error, we differentiate to obtain ...
*7.8The Bayes Estimator 273 continuous case — that a data value is equal toxwhenθis the value of the parameter. If the observed ...
274 Chapter 7: Parameter Estimation Now it can be shown that for integral valuesmandr ∫ 1 0 θm(1−θ)rdθ= m!r! (m+r+1)! (7.8.1) He ...
*7.8The Bayes Estimator 275 where f(x 1 ,...,xn|θ)= 1 (2π)n/2σ 0 n exp { − ∑n i= 1 (xi−θ)^2 /2σ 02 } p(θ)= 1 √ 2 πσ exp{−(θ−μ)^2 ...
276 Chapter 7: Parameter Estimation that it will be betweenμandμ+a? If the answer is positive, then we accept, as a working hypo ...
Problems 277 maximizingf(x 1 ,...,xn|θ); that is, it is just the maximum likelihood estimate ofθ[when it is constrained to be in ...
278 Chapter 7: Parameter Estimation Determine the maximum likelihood estimator ofθwhenX 1 ,...,Xnis a sample with density funct ...
Problems 279 Annual Floods of the Blackstone River (1929–1965) Flood Discharge Year (ft^3 /s) 1929 4,570 1930 1,970 1931 8,220 1 ...
280 Chapter 7: Parameter Estimation and .005, estimate the fraction of all exchangers whose plate spacings fall outside the spec ...
Problems 281 16.Suppose that when sampling from a normal population having an unknown meanμand unknown varianceσ^2 , we wish to ...
282 Chapter 7: Parameter Estimation deviation of $800, find a 90 percent confidence interval estimate of the mean cost per colli ...
Problems 283 98.8. Compute a 95 percent two-sided confidence interval for the mean carbon monoxide concentration. 28.A set of 10 ...
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