Introduction to Mathematical Statistics |
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Page 258
... function which yields the probability of rejecting the hypothesis under consideration . The value of the power function at a parameter point is called the power of the test at that point . 1 Definition 5. Let Ho denote an hypothesis ...
... function which yields the probability of rejecting the hypothesis under consideration . The value of the power function at a parameter point is called the power of the test at that point . 1 Definition 5. Let Ho denote an hypothesis ...
Page 260
... power function of the test . = 10.2 . Let X have a binomial distribution with parameters n = 10 and p = { p ; p = 1 , 4 } . The simple hypothesis Ho : p = is rejected , and the alternative simple hypothesis H1 : p = is accepted , if the ...
... power function of the test . = 10.2 . Let X have a binomial distribution with parameters n = 10 and p = { p ; p = 1 , 4 } . The simple hypothesis Ho : p = is rejected , and the alternative simple hypothesis H1 : p = is accepted , if the ...
Page 272
... power function K ( 0 ) , 00 , of this test . 1 2 1 4 10.17 . Let X have a p.d.f. of the form f ( x ; 0 ) = 1/0 , 0 < x < 0 , zero else- where . Let Y1 < Y2 < Y3 < Y1 denote the order statistics of a random sample of size 4 from this ...
... power function K ( 0 ) , 00 , of this test . 1 2 1 4 10.17 . Let X have a p.d.f. of the form f ( x ; 0 ) = 1/0 , 0 < x < 0 , zero else- where . Let Y1 < Y2 < Y3 < Y1 denote the order statistics of a random sample of size 4 from this ...
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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