Introduction to Mathematical Statistics |
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Page 256
... true , the probability of rejecting this true hypothesis Ho is . Many statisticians and research workers find it very undesirable to have such a high probability as assigned to this kind of mistake , namely , the rejection of Ho when Ho ...
... true , the probability of rejecting this true hypothesis Ho is . Many statisticians and research workers find it very undesirable to have such a high probability as assigned to this kind of mistake , namely , the rejection of Ho when Ho ...
Page 259
... true , that is , f ( x1 ; 4 ) ƒ ( x2 ; 4 ) = = 4 0 0 = 0.05 approximately . = 4 , the joint p.d.f. of X1 and X2 is ... true is 0.05 , and the probability of rejecting H。 when H。 is false is 0.31 . Since the significance level of this ...
... true , that is , f ( x1 ; 4 ) ƒ ( x2 ; 4 ) = = 4 0 0 = 0.05 approximately . = 4 , the joint p.d.f. of X1 and X2 is ... true is 0.05 , and the probability of rejecting H。 when H。 is false is 0.31 . Since the significance level of this ...
Page 325
... true . We have E ( X1 ) = μ + α1 , E ( X1 . ) μ + α¿ , E ( X .; ) = μ , and E ( X ) = μ , and E ( X ) = μ . Thus = the noncentrality parameter of Q4 / σ2 is b α Σμ - j = 1 μ ) 2 = = 0 , and the noncentrality parameter of Q5 / σ2 is Ž Ž ...
... true . We have E ( X1 ) = μ + α1 , E ( X1 . ) μ + α¿ , E ( X .; ) = μ , and E ( X ) = μ , and E ( X ) = μ . Thus = the noncentrality parameter of Q4 / σ2 is b α Σμ - j = 1 μ ) 2 = = 0 , and the noncentrality parameter of Q5 / σ2 is Ž Ž ...
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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