Introduction to Mathematical Statistics |
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Page 179
... consider certain functions of the order statistics . Let X1 , X2 , ... , X2 denote a random sample of size n from a distribution that has a positive and continuous p.d.f. ƒ ( x ) if and only if a < x < b ; and let F ( x ) denote the ...
... consider certain functions of the order statistics . Let X1 , X2 , ... , X2 denote a random sample of size n from a distribution that has a positive and continuous p.d.f. ƒ ( x ) if and only if a < x < b ; and let F ( x ) denote the ...
Page 272
... Consider a normal distribution of the form n ( 0 , 4 ) . The simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 : 00 is accepted if and only if the observed mean ≈ of a random sample of size 25 is ...
... Consider a normal distribution of the form n ( 0 , 4 ) . The simple hypothesis H 。: 0 = 0 is rejected , and the alternative composite hypothesis H1 : 00 is accepted if and only if the observed mean ≈ of a random sample of size 25 is ...
Page 330
... Consider the = = α2 = ... hypothesis Ho : μ1j μ + B , ( or Ho : α1 = αa = 0 ) . Show that a likelihood ratio test of Ho against all possible alternatives may be based , in the notation of Section 12.1 , on the F = ( b 1 ) ( Q2 / Q5 ) ...
... Consider the = = α2 = ... hypothesis Ho : μ1j μ + B , ( or Ho : α1 = αa = 0 ) . Show that a likelihood ratio test of Ho against all possible alternatives may be based , in the notation of Section 12.1 , on the F = ( b 1 ) ( Q2 / Q5 ) ...
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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