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 accept accordance Accordingly alternative approximately assume called cent Chapter complete compute Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given H₁ Hence hypothesis inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics parameter probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁