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 146
... section can be omitted at this point and Section 4.10 can be considered later . If this decision is made , only an example in Section 4.7 and a few exercises need be skipped because the bivariate normal distribution would not be known ...
... section can be omitted at this point and Section 4.10 can be considered later . If this decision is made , only an example in Section 4.7 and a few exercises need be skipped because the bivariate normal distribution would not be known ...
Page 481
... section . 10.34 . Verify the p.d.f. ( 2 ) of this section . 10.8 The Distributions of Certain Quadratic Forms Remark . It is essential that the reader have the background of the multivariate normal distribution as given in Section 4.10 ...
... section . 10.34 . Verify the p.d.f. ( 2 ) of this section . 10.8 The Distributions of Certain Quadratic Forms Remark . It is essential that the reader have the background of the multivariate normal distribution as given in Section 4.10 ...
Page 526
... Section 11.8 . Example 1. With the assumptions and the notation of this section , let m = 10 and n = 9. Let the observed values of X be as given in the first row and the observed values of Y as in the second row of the following display ...
... Section 11.8 . Example 1. With the assumptions and the notation of this section , let m = 10 and n = 9. Let the observed values of X be as given in the first row and the observed values of Y as in the second row of the following display ...
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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