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 179
... normal distribution with respective parameters με = 2.8 , μ 110 , σ2 = 0.16 , σ = 100 , and p = 0.6 . Compute : = ( a ) P ( 106 < Y < 124 ) . ( b ) P ( 106 < Y < 124 | X = 3.2 ) . 3.5.2 . Let X and Y have a bivariate normal distribution ...
... normal distribution with respective parameters με = 2.8 , μ 110 , σ2 = 0.16 , σ = 100 , and p = 0.6 . Compute : = ( a ) P ( 106 < Y < 124 ) . ( b ) P ( 106 < Y < 124 | X = 3.2 ) . 3.5.2 . Let X and Y have a bivariate normal distribution ...
Page 220
... distribution of Yn as n → ∞ . Exercises 4.3.14 and 4.3.16 are special instances of an important theorem that will ... normal distribution with mean μ and variance o2 , the random variable - Σ i = 1 Χ - ημ o√n √n ( Xn - μ ) = σ is ...
... distribution of Yn as n → ∞ . Exercises 4.3.14 and 4.3.16 are special instances of an important theorem that will ... normal distribution with mean μ and variance o2 , the random variable - Σ i = 1 Χ - ημ o√n √n ( Xn - μ ) = σ is ...
Page 291
... normal random variables . One of the most commonly used normal generators is a variant of the above procedure called the Marsaglia and Bray ( 1964 ) algorithm ; see Exercise 5.8.20 . □ Observations from a contaminated normal distribution ...
... normal random variables . One of the most commonly used normal generators is a variant of the above procedure called the Marsaglia and Bray ( 1964 ) algorithm ; see Exercise 5.8.20 . □ Observations from a contaminated normal distribution ...
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