Introduction to Mathematical Statistics |
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Page 260
... observed value of X1 , a random sample of size 1 , is less than or equal to 3. Find the power function of the test . = 10.3 . Let X1 , X2 be a random sample of size n = 2 from the distribution having p.d.f. ƒ ( x ; 0 ) ( 1/0 ) e ̄x / 0 ...
... observed value of X1 , a random sample of size 1 , is less than or equal to 3. Find the power function of the test . = 10.3 . Let X1 , X2 be a random sample of size n = 2 from the distribution having p.d.f. ƒ ( x ; 0 ) ( 1/0 ) e ̄x / 0 ...
Page 272
... observed values x1 , x2 , . . . , 10 of the 10 sample items are such that Σx , ≤ 1. Find the power function K ( 0 ) , 0 < 0 , of this test . 1 2 4 10.17 . Let X have a p.d.f. of the form f ( x ; 0 ) = 1/0 , 0 < x < 0 , zero else- where ...
... observed values x1 , x2 , . . . , 10 of the 10 sample items are such that Σx , ≤ 1. Find the power function K ( 0 ) , 0 < 0 , of this test . 1 2 4 10.17 . Let X have a p.d.f. of the form f ( x ; 0 ) = 1/0 , 0 < x < 0 , zero else- where ...
Page 306
... observations , the observed frequencies of these respective classifications are 86 , 35 , 26 , and 13 , are these data consistent with the Mendelian theory ? That is , test , with a = 0.01 , the hypothesis that the respective ...
... observations , the observed frequencies of these respective classifications are 86 , 35 , 26 , and 13 , are these data consistent with the Mendelian theory ? That is , test , with a = 0.01 , the hypothesis that the respective ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider 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 H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions 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 theorem unbiased statistic variance oČ w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ