Introduction to Mathematical Statistics |
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Page 128
... degrees of freedom . Find Pr ( T > 2.228 ) from Table IV . 4.29 . Let T have a t distribution with 14 degrees of freedom . Determine b so that Pr ( -b < T < b ) = 0.90 . 4.30 . Let F have an F distribution with parameters 1 and 2 . 1 ...
... degrees of freedom . Find Pr ( T > 2.228 ) from Table IV . 4.29 . Let T have a t distribution with 14 degrees of freedom . Determine b so that Pr ( -b < T < b ) = 0.90 . 4.30 . Let F have an F distribution with parameters 1 and 2 . 1 ...
Page 312
... degrees of freedom . Now a Σ . - Q2 = 6 1⁄2 ( Ã ̧ . – X ) 2 ≥ 0. In accordance with the theorem , Q1 and Q2 are i = 1 - stochastically independent , and Q2 / 02 has a chi - square distribution with ab 1 a ( b − 1 ) = a 1 degrees of ...
... degrees of freedom . Now a Σ . - Q2 = 6 1⁄2 ( Ã ̧ . – X ) 2 ≥ 0. In accordance with the theorem , Q1 and Q2 are i = 1 - stochastically independent , and Q2 / 02 has a chi - square distribution with ab 1 a ( b − 1 ) = a 1 degrees of ...
Page 313
... degrees of freedom . In the subsequent sections it will be seen that some likelihood ratio tests of certain statistical hypotheses can be based on these F statistics . EXERCISES 12.1 . In Example 2 , verify that Q = Q3 Q4 and that Q3 ...
... degrees of freedom . In the subsequent sections it will be seen that some likelihood ratio tests of certain statistical hypotheses can be based on these F statistics . EXERCISES 12.1 . In Example 2 , verify that Q = Q3 Q4 and that Q3 ...
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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