Introduction to Mathematical StatisticsThis classic book retains its outstanding ongoing features and continues to provide readers with excellent background material necessary for a successful understanding of mathematical statistics.Chapter topics cover classical statistical inference procedures in estimation and testing, and an in-depth treatment of sufficiency and testing theory—including uniformly most powerful tests and likelihood ratios. Many illustrative examples and exercises enhance the presentation of material throughout the book.For a more complete understanding of mathematical statistics. |
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Page 67
... continuous type with pdf f ( x ) , which is positive provided 0 < x < b < ∞ , and is equal to zero elsewhere . Show that E ( X ) = [ 1 − F ( x ) ] dx , where F ( x ) is the cdf of X. 1.9.20 . Let X be a random variable of the discrete ...
... continuous type with pdf f ( x ) , which is positive provided 0 < x < b < ∞ , and is equal to zero elsewhere . Show that E ( X ) = [ 1 − F ( x ) ] dx , where F ( x ) is the cdf of X. 1.9.20 . Let X be a random variable of the discrete ...
Page 94
... type because PX2 X1 ( 21 ) is nonnegative and ΣPX2 | X1 ( X2X1 ) = ΣPX1 , X2 ( X1 , X2 ) I2 X2 PX1 ( x1 ) 1 = PX1 ... continuous type and have the joint pdf fx1 , X2 ( x1 , x2 ) and the marginal probability density functions fx , ( x1 ) ...
... type because PX2 X1 ( 21 ) is nonnegative and ΣPX2 | X1 ( X2X1 ) = ΣPX1 , X2 ( X1 , X2 ) I2 X2 PX1 ( x1 ) 1 = PX1 ... continuous type and have the joint pdf fx1 , X2 ( x1 , x2 ) and the marginal probability density functions fx , ( x1 ) ...
Page 250
... continuous type . 5.2.27 . Find the smallest value of n for which P ( Y1 < §0.5 < Yn ) ≥ 0.99 , where Y1 < < Yn are the order statistics of a random sample of size n from a distribu- tion of the continuous type . ... 5.2.28 . Let Y1 ...
... continuous type . 5.2.27 . Find the smallest value of n for which P ( Y1 < §0.5 < Yn ) ≥ 0.99 , where Y1 < < Yn are the order statistics of a random sample of size n from a distribu- tion of the continuous type . ... 5.2.28 . Let Y1 ...
Contents
Some Elementary Statistical Inferences | 5 |
Multivariate Distributions | 73 |
Some Special Distributions | 133 |
Copyright | |
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Other editions - View all
Introduction to Mathematical Statistics Robert V. Hogg,Joseph W. McKean,Allen Thornton Craig No preview available - 2005 |
Introduction to Mathematical Statistics Robert V. Hogg,Hogg,Joseph W. McKean,Allen T. Craig No preview available - 2013 |
Common terms and phrases
approximate asymptotic Bayes bootstrap C₁ C₂ chi-square distribution compute conditional pdf confidence interval Consider continuous random variable continuous type correlation coefficient critical region defined degrees of freedom denote a random determine discrete random variable discrete type discussed equal equation Example Exercise Find Fx(x gamma distribution given H₁ Hence independent random variables inequality integral joint pdf Let the random Let X1 Let Y₁ likelihood function linear marginal pdf matrix median MVUE normal distribution observations obtain order statistics p-value P(C₁ p₁ pdf f(x pdf of Y₁ Poisson distribution Proof random sample random variables X1 random vector respectively result S-PLUS sample mean sample space sequence Show significance level subsets sufficient statistic Suppose t-distribution test statistic Theorem unbiased estimator Wilcoxon X₁ X1 and X2 Y₁ Y₂ zero elsewhere σ²