Introduction to Mathematical Statistics |
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Page 260
... simple hypothesis Ho : 0 = 1 against the alternative simple hypothesis H1 : 0 2 use a random sample X1 , X2 of size n = 2 and define the critical region to be C = { ( x1 , x2 ) ; 3 / ( 4x1 ) ≤ x2 } . Find the power function of the test ...
... simple hypothesis Ho : 0 = 1 against the alternative simple hypothesis H1 : 0 2 use a random sample X1 , X2 of size n = 2 and define the critical region to be C = { ( x1 , x2 ) ; 3 / ( 4x1 ) ≤ x2 } . Find the power function of the test ...
Page 268
... simple hypothesis H。 against an alternative composite hypothesis H1 . We begin with an example . Example 1. Consider the p.d.f. 1 ƒ ( x ; 0 ) = = e− e - x10 0 < x < ∞∞ , = 0 elsewhere , = 2 of Example 2 , p . 258. It is desired to ...
... simple hypothesis H。 against an alternative composite hypothesis H1 . We begin with an example . Example 1. Consider the p.d.f. 1 ƒ ( x ; 0 ) = = e− e - x10 0 < x < ∞∞ , = 0 elsewhere , = 2 of Example 2 , p . 258. It is desired to ...
Page 273
... simple hypothesis Ho : 01 01 , 02 02 > 0 , against the alternative simple hypothesis H1 : 01 = 0 < 01 , 02 = 021⁄2 > 02. Is this a uniformly most powerful critical 01 region for testing Ho : 01 01 , 02 02 > 0 , against H1 : 01 < 01 , 02 > ...
... simple hypothesis Ho : 01 01 , 02 02 > 0 , against the alternative simple hypothesis H1 : 01 = 0 < 01 , 02 = 021⁄2 > 02. Is this a uniformly most powerful critical 01 region for testing Ho : 01 01 , 02 02 > 0 , against H1 : 01 < 01 , 02 > ...
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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