Introduction to Mathematical Statistics |
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Page 155
... interval ( − 20 / √n , x + 20 / √n ) a 95.4 per cent confidence interval for μ . The number 0.954 is called the confidence coefficient . The confidence coefficient is equal to the probability that the random interval includes the ...
... interval ( − 20 / √n , x + 20 / √n ) a 95.4 per cent confidence interval for μ . The number 0.954 is called the confidence coefficient . The confidence coefficient is equal to the probability that the random interval includes the ...
Page 158
... interval ( -5.16 , 6.76 ) is a 90 per cent confidence interval for = EXERCISES = = - με H2 . 5.6 . Let the observed value of the mean X of a random sample of size 20 from a distribution which is n ( μ , 80 ) be 81.2 . Find a 95 per cent ...
... interval ( -5.16 , 6.76 ) is a 90 per cent confidence interval for = EXERCISES = = - με H2 . 5.6 . Let the observed value of the mean X of a random sample of size 20 from a distribution which is n ( μ , 80 ) be 81.2 . Find a 95 per cent ...
Page 162
... confidence interval for 02/02 . EXERCISES 5.14 . If 8.6 , 7.9 , 8.3 , 6.4 , 8.4 , 9.8 , 7.2 , 7.8 , 7.5 are the observed values of a random sample of size ... interval estimation . 162 Interval Estimation [ Ch . 5 Bayesian Interval Estimates.
... confidence interval for 02/02 . EXERCISES 5.14 . If 8.6 , 7.9 , 8.3 , 6.4 , 8.4 , 9.8 , 7.2 , 7.8 , 7.5 are the observed values of a random sample of size ... interval estimation . 162 Interval Estimation [ Ch . 5 Bayesian Interval Estimates.
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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