Introduction to Mathematical Statistics |
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Page 4
... writing A2 . If A1 C A2 and also A2 A1 , the two sets have the same elements , and this is indicated by writing A1 = A2 . A1 1 2 . 1 = Example 1. Let A1 { x ; 0 ≤ x ≤ 1 } and A2 = { x ; -1 ≤ x ≤ 2 } . Here the one - dimensional set ...
... writing A2 . If A1 C A2 and also A2 A1 , the two sets have the same elements , and this is indicated by writing A1 = A2 . A1 1 2 . 1 = Example 1. Let A1 { x ; 0 ≤ x ≤ 1 } and A2 = { x ; -1 ≤ x ≤ 2 } . Here the one - dimensional set ...
Page 13
... write P ( A ) = the probability that XEA = Pr ( X = A ) . If the outcome of a random experiment is expressed as an ordered pair of numbers , we can represent this outcome by the two random variables X and Y. Then the sample space is a ...
... write P ( A ) = the probability that XEA = Pr ( X = A ) . If the outcome of a random experiment is expressed as an ordered pair of numbers , we can represent this outcome by the two random variables X and Y. Then the sample space is a ...
Page 344
... write L'AL diag [ a1 , a2 , ... , an ] . In integral ( 3 ) , we shall change the vari- ables of integration from y1 , Y2 , ... , Yn to Z1 , Z2 , ... , Zn by writing y = Lz , where z ' = [ 21 , 22 , ... , Zn ] . The Jacobian of the ...
... write L'AL diag [ a1 , a2 , ... , an ] . In integral ( 3 ) , we shall change the vari- ables of integration from y1 , Y2 , ... , Yn to Z1 , Z2 , ... , Zn by writing y = Lz , where z ' = [ 21 , 22 , ... , Zn ] . The Jacobian of the ...
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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