Introduction to Mathematical Statistics |
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Page 75
... stochastic independence of X1 , X2 , ... , Xn Remark . If X1 , X2 , and X , are mutually stochastically independent , they are pairwise stochastically independent ( that is , X , and X ,, i ‡ j , where i , j = 1 , 2 , 3 are stochastically ...
... stochastic independence of X1 , X2 , ... , Xn Remark . If X1 , X2 , and X , are mutually stochastically independent , they are pairwise stochastically independent ( that is , X , and X ,, i ‡ j , where i , j = 1 , 2 , 3 are stochastically ...
Page 233
... stochastically independent of the sufficient statistic Y1 , as was to be proved . 1 = If it is assumed that a statistic Z is stochastically independent of a statistic Y1 , then , of course , g2 ( 2 ) h ( zy1 ) . It is interesting to ...
... stochastically independent of the sufficient statistic Y1 , as was to be proved . 1 = If it is assumed that a statistic Z is stochastically independent of a statistic Y1 , then , of course , g2 ( 2 ) h ( zy1 ) . It is interesting to ...
Page 358
... stochastically independent , determine a1 , a2 , aз , and a4 . == 13.13 . Let A be the real symmetric matrix of a quadratic form Q in the items of a random sample of size n from a distribution which is n ( 0 , o2 ) . Given that Q and ...
... stochastically independent , determine a1 , a2 , aз , and a4 . == 13.13 . Let A be the real symmetric matrix of a quadratic form Q in the items of a random sample of size n from a distribution which is n ( 0 , o2 ) . Given that Q and ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ