Introduction to Mathematical Statistics |
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Page 1
... outcome of which cannot be predicted with certainty , but the experiment is of such a nature that the collection of every possible outcome can be described prior to its performance . If this kind of experiment can be repeated under the ...
... outcome of which cannot be predicted with certainty , but the experiment is of such a nature that the collection of every possible outcome can be described prior to its performance . If this kind of experiment can be repeated under the ...
Page 2
... outcome is one of the two numbers zero and one ; that is , the sample space is the collection of these two numbers . Example 2. In the cast of one red die and one white die , let the outcome be the ordered pair ( number of spots up on ...
... outcome is one of the two numbers zero and one ; that is , the sample space is the collection of these two numbers . Example 2. In the cast of one red die and one white die , let the outcome be the ordered pair ( number of spots up on ...
Page 13
... outcome of a random experiment can be expressed by a single number . Then the sample space ✓ can be represented by a set of points on a directed line . If we denote the outcome by the sym- bol X , we call X a random variable . If A is ...
... outcome of a random experiment can be expressed by a single number . Then the sample space ✓ can be represented by a set of points on a directed line . If we denote the outcome by the sym- bol X , we call X a random variable . If A is ...
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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