Introduction to Mathematical Statistics |
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Page 5
... Example 1. Then A1UA2 = A2 . Example 5. Let A2 = 0. Then A , U A2 = A1 for every set A1 . Example 6. For every set A , AUA A. = Example 7. Let Ak = { x ; 1 / ( k + 1 ) ≤ x ≤ 1 } , k = 1 , 2 , 3 , .... Then A1UA2UA U { x ; 0 < x ≤ 1 } ...
... Example 1. Then A1UA2 = A2 . Example 5. Let A2 = 0. Then A , U A2 = A1 for every set A1 . Example 6. For every set A , AUA A. = Example 7. Let Ak = { x ; 1 / ( k + 1 ) ≤ x ≤ 1 } , k = 1 , 2 , 3 , .... Then A1UA2UA U { x ; 0 < x ≤ 1 } ...
Page 6
... Example 14. Let the number of heads , in tossing a coin four times , be denoted by x . Of necessity , the number of heads will be one of the numbers 0 , 1 , 2 , 3 , 4. Here , then , the space is the set = { x ; x = 0 , 1 , 2 , 3 , 4 } ...
... Example 14. Let the number of heads , in tossing a coin four times , be denoted by x . Of necessity , the number of heads will be one of the numbers 0 , 1 , 2 , 3 , 4. Here , then , the space is the set = { x ; x = 0 , 1 , 2 , 3 , 4 } ...
Page 293
... Example 1 , let n = 10 , and let the experimental values of the random variables yield ♬ = 0.6 and 1⁄2 ( ~ , 10 - x ) 2 - 3.6 . If the test derived 01 in that example is used , do we accept or reject H 。: 01 = 0 at the 5 per cent ...
... Example 1 , let n = 10 , and let the experimental values of the random variables yield ♬ = 0.6 and 1⁄2 ( ~ , 10 - x ) 2 - 3.6 . If the test derived 01 in that example is used , do we accept or reject H 。: 01 = 0 at the 5 per cent ...
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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