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 r ...
... 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 r ...
Page 296
... degrees of freedom . Since , when Ho is true , npo is the expected value of X1 , one would feel intuitively that experimental values of Qk - 1 should not be too large if Ho is true . With this in mind , we may use Table II of Appendix B ...
... degrees of freedom . Since , when Ho is true , npo is the expected value of X1 , one would feel intuitively that experimental values of Qk - 1 should not be too large if Ho is true . With this in mind , we may use Table II of Appendix B ...
Page 451
... degrees of freedom ; and Q1 / [ o2 ( b - 1 ) ] = Q4 / ( b - 1 ) Qs / [ o2 ( a− 1 ) ( b − 1 ) ] Qs / ( a − 1 ) ( b − 1 ) - - — has an F - distribution with b - 1 and ( a− 1 ) ( b − 1 ) degrees of freedom . In the subsequent ...
... degrees of freedom ; and Q1 / [ o2 ( b - 1 ) ] = Q4 / ( b - 1 ) Qs / [ o2 ( a− 1 ) ( b − 1 ) ] Qs / ( a − 1 ) ( b − 1 ) - - — has an F - distribution with b - 1 and ( a− 1 ) ( b − 1 ) degrees of freedom . In the subsequent ...
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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