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 188
... consider some other problems that are encountered when transforming variables . Let X have the Cauchy p.d.f. 1 f ( x ) = π ( 1 + x2 ) , < ∞ , and let Y = X2 . We seek the p.d.f. g ( y ) of Y. Consider the transformation y = x2 . This ...
... consider some other problems that are encountered when transforming variables . Let X have the Cauchy p.d.f. 1 f ( x ) = π ( 1 + x2 ) , < ∞ , and let Y = X2 . We seek the p.d.f. g ( y ) of Y. Consider the transformation y = x2 . This ...
Page 448
... consider each row as being a random sample of size b from the given distribution ; and we may consider each column as being a random sample of size a from the given distribution . We now define a + b + 1 statistics . They are a b Σ Σ Χ ...
... consider each row as being a random sample of size b from the given distribution ; and we may consider each column as being a random sample of size a from the given distribution . We now define a + b + 1 statistics . They are a b Σ Σ Χ ...
Page 501
... consider certain functions of the order statistics . Let X1 , X2 , . . . , X , denote a random sample of size n from a distribution that has a positive and continuous p.d.f. f ( x ) if and only if a < x < b ; and let F ( x ) denote the ...
... consider certain functions of the order statistics . Let X1 , X2 , . . . , X , denote a random sample of size n from a distribution that has a positive and continuous p.d.f. f ( x ) if and only if a < x < b ; and let F ( x ) denote the ...
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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 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