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Page 72
Robert V. Hogg, Allen Thornton Craig. Theorem 3. Let the stochastically independent random variables X1 and X2 have the marginal probability ... stochastically independent , 72 Conditional Probability and Stochastic Independence [ Ch . 2.
Robert V. Hogg, Allen Thornton Craig. Theorem 3. Let the stochastically independent random variables X1 and X2 have the marginal probability ... stochastically independent , 72 Conditional Probability and Stochastic Independence [ Ch . 2.
Page 75
... independence of X1 , X2 , . . . , Xn · 3 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 ...
... independence of X1 , X2 , . . . , Xn · 3 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 236
... stochastically independent . n 1 n − Y1 ) . Find the moment- - ( b ) Write ( Y , — 9 ) 0 ) = n ( Y1 - 10 ) + 2 ( ૐ ( Y , e ) and n ( Y1 0 ) . Use the fact that Y1 1 generating functions of Σ ( Y ; n and Σ ( Υ 1 i ― Y1 ) are stochastically ...
... stochastically independent . n 1 n − Y1 ) . Find the moment- - ( b ) Write ( Y , — 9 ) 0 ) = n ( Y1 - 10 ) + 2 ( ૐ ( Y , e ) and n ( Y1 0 ) . Use the fact that Y1 1 generating functions of Σ ( Y ; n and Σ ( Υ 1 i ― Y1 ) are stochastically ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²