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 109
... random variables X1 and X2 have the joint pdf f ( x1 , x2 ) ( joint pmf p ( x1 , x2 ) ) and the marginal pdfs ( pmfs ) ƒ1 ( x1 ) ( p1 ( x1 ) ) and f2 ( x2 ) ( P2 ( x2 ) ) , respectively . The random variables X1 and X2 are said to be ...
... random variables X1 and X2 have the joint pdf f ( x1 , x2 ) ( joint pmf p ( x1 , x2 ) ) and the marginal pdfs ( pmfs ) ƒ1 ( x1 ) ( p1 ( x1 ) ) and f2 ( x2 ) ( P2 ( x2 ) ) , respectively . The random variables X1 and X2 are said to be ...
Page 114
... X1 and X2 are inde- pendent random variables . □ EXERCISES 2.5.1 . Show that the random variables X1 and X2 with joint pdf f ( x1 , x2 ) = { 0 12x12 ( 1-2 ) 0 < 1 < 1 , 0 < x2 < 1 elsewhere are independent . -x1 - X2 , 0 < 2.5.2 . If the ...
... X1 and X2 are inde- pendent random variables . □ EXERCISES 2.5.1 . Show that the random variables X1 and X2 with joint pdf f ( x1 , x2 ) = { 0 12x12 ( 1-2 ) 0 < 1 < 1 , 0 < x2 < 1 elsewhere are independent . -x1 - X2 , 0 < 2.5.2 . If the ...
Page 118
... X1 1. The joint conditional pdf of any n 1 random variables , say X1 , ... , Xi - 1 , Xi + 1 , ... , Xn , given X1 = x , is defined as the joint pdf of X1 , ... , Xn divided by the marginal pdf fi ( xi ) , provided that f ( x ) > 0 ...
... X1 1. The joint conditional pdf of any n 1 random variables , say X1 , ... , Xi - 1 , Xi + 1 , ... , Xn , given X1 = x , is defined as the joint pdf of X1 , ... , Xn divided by the marginal pdf fi ( xi ) , provided that f ( x ) > 0 ...
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