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. |
From inside the book
Results 1-3 of 84
Page 103
... Accordingly , X , and X2 are independent . If we now refer to Example 1 , we see that the joint p.d.f. f ( x1 , x2 ) = x1 + x2 , 0 < x < 1 , 0 < x2 < 1 , = 0 elsewhere , cannot be written as the product of a nonnegative function of x ...
... Accordingly , X , and X2 are independent . If we now refer to Example 1 , we see that the joint p.d.f. f ( x1 , x2 ) = x1 + x2 , 0 < x < 1 , 0 < x2 < 1 , = 0 elsewhere , cannot be written as the product of a nonnegative function of x ...
Page 286
... Accordingly , the power of the test when X2 Ho is true is given by 0 Pr ( Y≥ 9.5 ) = 1 − Pr ( Y < 9.5 ) 10.95 0.05 , = = - from Table II of Appendix B. When the hypothesis H , is true , the random variable X / 2 is x2 ( 2 ) ; so the ...
... Accordingly , the power of the test when X2 Ho is true is given by 0 Pr ( Y≥ 9.5 ) = 1 − Pr ( Y < 9.5 ) 10.95 0.05 , = = - from Table II of Appendix B. When the hypothesis H , is true , the random variable X / 2 is x2 ( 2 ) ; so the ...
Page 378
... Accordingly , - E “ Ə2 ln ƒ ( X ; 0 ) 202 0 1 = 03 202 - = 1 202 - Thus the Rao - Cramér lower bound is 202 / n . Now nS2 / 0 is x2 ( n − 1 ) , so the variance of nS2 / 0 is 2 ( n − 1 ) . Accordingly , the variance of nS2 / ( n − 1 ) ...
... Accordingly , - E “ Ə2 ln ƒ ( X ; 0 ) 202 0 1 = 03 202 - = 1 202 - Thus the Rao - Cramér lower bound is 202 / n . Now nS2 / 0 is x2 ( n − 1 ) , so the variance of nS2 / 0 is 2 ( n − 1 ) . Accordingly , the variance of nS2 / ( n − 1 ) ...
Other editions - View all
Common terms and phrases
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