Introduction to Mathematical Statistics |
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Page 180
... Equation 0 < z < 1 , the marginal p.d.f. of Zk ( 2 ) , Section 6.1 , the following beta p.d.f. ( 1 ) hx ( ZK ) = ( k n ! 1 ) ! ( n - k ) ! zk - 1 ( 1 - zx ) -k , 0 < k < 1 , = 0 elsewhere . = Moreover , the joint p.d.f. of Z 、 and in ...
... Equation 0 < z < 1 , the marginal p.d.f. of Zk ( 2 ) , Section 6.1 , the following beta p.d.f. ( 1 ) hx ( ZK ) = ( k n ! 1 ) ! ( n - k ) ! zk - 1 ( 1 - zx ) -k , 0 < k < 1 , = 0 elsewhere . = Moreover , the joint p.d.f. of Z 、 and in ...
Page 181
... Equation ( 4 ) is precisely the probability of at least k " successes " throughout n independent trials , each trial with prob- ability p of success . One purpose of our derivation of Equation ( 4 ) is to point out the fact that a ...
... Equation ( 4 ) is precisely the probability of at least k " successes " throughout n independent trials , each trial with prob- ability p of success . One purpose of our derivation of Equation ( 4 ) is to point out the fact that a ...
Page 357
... equation B , AI - - - - - - = 0. Since B1 = I – A1 , this equation can be written as | I – A , - XI | = 0 . Thus we have A , − ( 1 − λ ) I | = 0. But each root of the last equation is one minus a characteristic number of A ,. Since B ...
... equation B , AI - - - - - - = 0. Since B1 = I – A1 , this equation can be written as | I – A , - XI | = 0 . Thus we have A , − ( 1 − λ ) I | = 0. But each root of the last equation is one minus a characteristic number of A ,. Since B ...
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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 o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ