Introduction to Mathematical Statistics |
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Page 12
... Definition 7 , P ( A2 ) = P ( A1 ) + P ( A * ~ A 2 ) . However , from ( a ) of Definition 7 , P ( A * ~ A2 ) ≥ 0 ; accordingly , P ( A2 ) ≥ P ( A1 ) . Theorem 4. For each AA , 0 ≤ P ( A ) ≤ 1 . Proof . Since 0 CAC , we have by ...
... Definition 7 , P ( A2 ) = P ( A1 ) + P ( A * ~ A 2 ) . However , from ( a ) of Definition 7 , P ( A * ~ A2 ) ≥ 0 ; accordingly , P ( A2 ) ≥ P ( A1 ) . Theorem 4. For each AA , 0 ≤ P ( A ) ≤ 1 . Proof . Since 0 CAC , we have by ...
Page 205
... definition . Definition 1. Any statistic whose mathematical expectation is equal to a parameter 0 is called an unbiased statistic for the parameter 0 . Otherwise the statistic is said to be biased . = = Now it would seem that if Y1 = u1 ...
... definition . Definition 1. Any statistic whose mathematical expectation is equal to a parameter 0 is called an unbiased statistic for the parameter 0 . Otherwise the statistic is said to be biased . = = Now it would seem that if Y1 = u1 ...
Page 257
... defined . Definition 1. A statistical hypothesis is an assertion about the dis- tribution of one or more random variables . If the statistical hypothesis completely specifies the distribution , it is called a simple statistical ...
... defined . Definition 1. A statistical hypothesis is an assertion about the dis- tribution of one or more random variables . If the statistical hypothesis completely specifies the distribution , it is called a simple statistical ...
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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