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 241
... positive integer n . Let c denote a constant which does not depend upon n . The sequence Yn n = 1 , 2 , 3 , ... , converges in probability to the constant c if and only if the limiting distribution of Y , is degenerate at y = c . n n ...
... positive integer n . Let c denote a constant which does not depend upon n . The sequence Yn n = 1 , 2 , 3 , ... , converges in probability to the constant c if and only if the limiting distribution of Y , is degenerate at y = c . n n ...
Page 253
... integer . The sum of the original 48 numbers is approximated by the sum of these integers . If we assume that the ... positive integer n . Let Un converge in probability to the constant c 0. The random variable Un / c converges in ...
... integer . The sum of the original 48 numbers is approximated by the sum of these integers . If we assume that the ... positive integer n . Let Un converge in probability to the constant c 0. The random variable Un / c converges in ...
Page 335
... positive probability density and the function R ( y , ) do not depend upon 0 ... integer ) is a random sample from a distribution with p.d.f. f ( x ; 0 ) ... positive number . This is a regular case of the exponential class with p ( 0 ) ...
... positive probability density and the function R ( y , ) do not depend upon 0 ... integer ) is a random sample from a distribution with p.d.f. f ( x ; 0 ) ... positive number . This is a regular case of the exponential class with p ( 0 ) ...
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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