Introduction to Mathematical Statistics |
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Page 11
... subset of ✓ , then P ( A ) is the prob- ability that the outcome of the random experiment is an element of A. Henceforth it will be tacitly assumed that the structure of each set A is sufficiently simple to allow the computation . We ...
... subset of ✓ , then P ( A ) is the prob- ability that the outcome of the random experiment is an element of A. Henceforth it will be tacitly assumed that the structure of each set A is sufficiently simple to allow the computation . We ...
Page 13
... subset of A , we would write P ( A ) = the probability that X e A = Pr ( X Є 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 ...
... subset of A , we would write P ( A ) = the probability that X e A = Pr ( X Є 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 ...
Page 50
... subset A1 of the sample space ✓ . This means that , for our purposes , the sample space is effectively the subset A1 . We are now confronted with the problem of defining a probability set function with A1 as the " new " sample space ...
... subset A1 of the sample space ✓ . This means that , for our purposes , the sample space is effectively the subset A1 . We are now confronted with the problem of defining a probability set function with A1 as the " new " sample space ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²