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 164
... x x = 0 , 1 , 2 , 3 , 3 x ! ( 3x ) ! 3 0 A elsewhere . B ye B , We seek the p.d.f. g ( y ) of the random variable Y = X2 . The transformation y = u ( x ) ... random variables Y1 = 164 Distributions of Functions of Random Variables [ Ch . 4.
... x x = 0 , 1 , 2 , 3 , 3 x ! ( 3x ) ! 3 0 A elsewhere . B ye B , We seek the p.d.f. g ( y ) of the random variable Y = X2 . The transformation y = u ( x ) ... random variables Y1 = 164 Distributions of Functions of Random Variables [ Ch . 4.
Page 447
... X 2 + · • + X2 ) n - 2/2 ( x , x 2 + · · · + X , XX , + · · · + Xn ~ 1 Xn ) n X1Xn + - is a quadratic form in the n variables X1 , X2 , ... , X. If the sample arises from a distribution that is N ( u , o2 ) , we know that the random ...
... X 2 + · • + X2 ) n - 2/2 ( x , x 2 + · · · + X , XX , + · · · + Xn ~ 1 Xn ) n X1Xn + - is a quadratic form in the n variables X1 , X2 , ... , X. If the sample arises from a distribution that is N ( u , o2 ) , we know that the random ...
Page 518
... xx yyyyyyy . To us , this strongly suggests that F ( z ) > G ( z ) . For if , in fact , F ( z ) = G ( z ) for all z , we would anticipate a greater number of runs . And if the first run of five values ... random variable R equal the number of ...
... xx yyyyyyy . To us , this strongly suggests that F ( z ) > G ( z ) . For if , in fact , F ( z ) = G ( z ) for all z , we would anticipate a greater number of runs . And if the first run of five values ... random variable R equal the number of ...
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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. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²