Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 58
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
... random interval includes the point o2 is Y Pr ( 3.25 << 20.5 ) . 1 / 20.5 ) = 1002. Accord- where Y / o2 is x2 ( 10 ) . From Table II in the Appendix , this probability is found to be 0.95 . The length of the random interval is Y ( 1 ...
... random interval includes the point o2 is Y Pr ( 3.25 << 20.5 ) . 1 / 20.5 ) = 1002. Accord- where Y / o2 is x2 ( 10 ) . From Table II in the Appendix , this probability is found to be 0.95 . The length of the random interval is Y ( 1 ...
Page 154
... random experiment is a random variable that has a normal distribution with known variance o2 but unknown mean μ ... interval ( X – 20 / √ñ , X + 20 / Vn ) contains the fixed ( but unknown ) mean μ . That is , Pr ( X - 20 20 < μ < Ï + = 0.954 ...
... random experiment is a random variable that has a normal distribution with known variance o2 but unknown mean μ ... interval ( X – 20 / √ñ , X + 20 / Vn ) contains the fixed ( but unknown ) mean μ . That is , Pr ( X - 20 20 < μ < Ï + = 0.954 ...
Other editions - View all
Common terms and phrases
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