Introduction to Mathematical Statistics |
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Page 151
Robert V. Hogg, Allen Thornton Craig. CHAPTER 5 Interval Estimation 5.1 Random Intervals Р = An interval , at least one of whose end points is a random variable , will be called a random interval . Let X denote a random variable and ...
Robert V. Hogg, Allen Thornton Craig. CHAPTER 5 Interval Estimation 5.1 Random Intervals Р = An interval , at least one of whose end points is a random variable , will be called a random interval . Let X denote a random variable and ...
Page 153
... interval ( Y / 20.5 , Y / 3.25 ) includes the point o2 ? We know that Y / o2 is x2 ( 10 ) . Moreover , the events Y ... Intervals for Means 153 Confidence Intervals for Means.
... interval ( Y / 20.5 , Y / 3.25 ) includes the point o2 ? We know that Y / o2 is x2 ( 10 ) . Moreover , the events Y ... Intervals for Means 153 Confidence Intervals for Means.
Page 162
... interval s2 = 5 ( 35.6 ) / 4 ( ( 4.72 ) 10 ( 20.0 ) / 9 ' ( 8.90 ) 5 ( 35.6 ) / 4 10 ( 20.0 ) / 9 or ( 0.4 , 17.8 ) is a 95 per cent confidence interval ... interval estimation . 162 Interval Estimation [ Ch . 5 Bayesian Interval Estimates.
... interval s2 = 5 ( 35.6 ) / 4 ( ( 4.72 ) 10 ( 20.0 ) / 9 ' ( 8.90 ) 5 ( 35.6 ) / 4 10 ( 20.0 ) / 9 or ( 0.4 , 17.8 ) is a 95 per cent confidence interval ... 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