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
... percent 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 ...
... percent 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 ...
Page 274
... percent confidence interval for μ . Using the fact that the sample mean of the observations , X , is approximately N ( μ , o2 / n ) , we see that the interval given by ± 1.96 ( 15 / √√n ) will serve as an approximate 95 percent ...
... percent confidence interval for μ . Using the fact that the sample mean of the observations , X , is approximately N ( μ , o2 / n ) , we see that the interval given by ± 1.96 ( 15 / √√n ) will serve as an approximate 95 percent ...
Page 275
... percent 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 ...
... percent 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 ...
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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. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²