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 85
Page 247
... theorem called the central limit theorem . A special case of this theorem asserts the remarkable and important fact that if X1 , X2 , ... , X , denote the observations of a random sample of size n from any distribution having positive ...
... theorem called the central limit theorem . A special case of this theorem asserts the remarkable and important fact that if X1 , X2 , ... , X , denote the observations of a random sample of size n from any distribution having positive ...
Page 255
... Theorem 4 , ( Y / n ) ( 1 − Y2 / n ) / [ p ( 1 − p ) ] converges in probability to 1 , and Theorem 5 asserts that the following does also : Vn = ( Y / n ) ( 1 — Y / n ) p ( 1 − p ) = n Thus , in accordance with Theorem 6 , the ratio ...
... Theorem 4 , ( Y / n ) ( 1 − Y2 / n ) / [ p ( 1 − p ) ] converges in probability to 1 , and Theorem 5 asserts that the following does also : Vn = ( Y / n ) ( 1 — Y / n ) p ( 1 − p ) = n Thus , in accordance with Theorem 6 , the ratio ...
Page 489
... Theorem 2 , we have V = σ2I , so that AVB = Aσ2IB = σ2AB 0 . - We shall next prove Theorem 1 that was stated in Section 10.1 . 1 • where Q , Theorem 4. Let Q = Q1 + ··· + Qk - 1 + Qk , Q1 , ... , Qk - 1 , Qk are k + 1 random variables ...
... Theorem 2 , we have V = σ2I , so that AVB = Aσ2IB = σ2AB 0 . - We shall next prove Theorem 1 that was stated in Section 10.1 . 1 • where Q , Theorem 4. Let Q = Q1 + ··· + Qk - 1 + Qk , Q1 , ... , Qk - 1 , Qk are k + 1 random variables ...
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 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