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 185
... degrees of freedom . Find Pr ( | T | > 2.228 ) from Table IV . 4.41 . Let T have a t - distribution with 14 degrees of freedom . Determine b so that Pr ( -b < T < b ) = 0.90 . 4.42 . Let F have an F - distribution with parameters r1 and ...
... degrees of freedom . Find Pr ( | T | > 2.228 ) from Table IV . 4.41 . Let T have a t - distribution with 14 degrees of freedom . Determine b so that Pr ( -b < T < b ) = 0.90 . 4.42 . Let F have an F - distribution with parameters r1 and ...
Page 422
... degrees of freedom . The hypothesis that ( 01 , 02 , 03 , 04 ) € @ is rejected if the computed F≤ c , or if the computed F≥ c2 . The constants c1 and c2 are usually selected so that , if 0 , = 0 . α1 > 2 Pr ( F ≤ c , ) = Pr ( F ...
... degrees of freedom . The hypothesis that ( 01 , 02 , 03 , 04 ) € @ is rejected if the computed F≤ c , or if the computed F≥ c2 . The constants c1 and c2 are usually selected so that , if 0 , = 0 . α1 > 2 Pr ( F ≤ c , ) = Pr ( F ...
Page 450
... degrees of freedom . – j = 1 Because the X , are independent , Q1 / 02 is the sum of a independent random variables , each having a chi - square distribution with b - 1 degrees of freedom . Hence Q1 / 2 has a chi - square distribution ...
... degrees of freedom . – j = 1 Because the X , are independent , Q1 / 02 is the sum of a independent random variables , each having a chi - square distribution with b - 1 degrees of freedom . Hence Q1 / 2 has a chi - square distribution ...
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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 g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ 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 sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²