Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 270
... confidence interval for μ . The number 0.954 is called the confidence coefficient . The confidence coefficient is equal to the probability that the random interval includes the parameter . One may , of course , obtain an 80 , a 90 , or ...
... confidence interval for μ . The number 0.954 is called the confidence coefficient . The confidence coefficient is equal to the probability that the random interval includes the parameter . One may , of course , obtain an 80 , a 90 , or ...
Page 275
... confidence interval for μ if this interval is based on the random variable 9 ( X - μ ) / σ . ( b ) If σ is unknown , find the expected value of the length of a 95 percent confidence interval for μ if this interval is based on the random ...
... confidence interval for μ if this interval is based on the random variable 9 ( X - μ ) / σ . ( b ) If σ is unknown , find the expected value of the length of a 95 percent confidence interval for μ if this interval is based on the random ...
Page 276
... confidence interval for 0 ? 6.28 . Let X1 , X2 , ... , X , be a random sample from N ( μ , o2 ) , where both parameters μ and 2 are unknown . A confidence interval for o2 can be found as follows . We know that nS2 / o2 is x2 ( n − 1 ) ...
... confidence interval for 0 ? 6.28 . Let X1 , X2 , ... , X , be a random sample from N ( μ , o2 ) , where both parameters μ and 2 are unknown . A confidence interval for o2 can be found as follows . We know that nS2 / o2 is x2 ( n − 1 ) ...
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²