Introduction to Mathematical Statistics |
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Page 158
... 9 5.12 . Let X1 , X2 , . . . , X , be a random sample of size 9 from a distribution which is n ( μ , o2 ) . ( a ) If σ is known , find the length of a 95 per cent confidence interval for μ if this interval is based on the random variable √ ...
... 9 5.12 . Let X1 , X2 , . . . , X , be a random sample of size 9 from a distribution which is n ( μ , o2 ) . ( a ) If σ is known , find the length of a 95 per cent confidence interval for μ if this interval is based on the random variable √ ...
Page 236
... statistic Y1 for 0 are stochastically independent . n 1 n − Y1 ) . Find the moment- - ( b ) Write ( Y , — 9 ) 0 ) = n ( Y1 - 10 ) + 2 ( ૐ ( Y , e ) and n ( Y1 0 ) . Use the fact that Y1 1 generating functions of Σ ( Y ; n and Σ ( Υ 1 ...
... statistic Y1 for 0 are stochastically independent . n 1 n − Y1 ) . Find the moment- - ( b ) Write ( Y , — 9 ) 0 ) = n ( Y1 - 10 ) + 2 ( ૐ ( Y , e ) and n ( Y1 0 ) . Use the fact that Y1 1 generating functions of Σ ( Y ; n and Σ ( Υ 1 ...
Page 237
Robert V. Hogg, Allen Thornton Craig. CHAPTER 9 Point Estimation 9.1 The Rao - Cramér Inequality In Chapter 8 , we used the problem of point estimation of a param- eter to motivate the study of sufficient statistics . In that chapter we ...
Robert V. Hogg, Allen Thornton Craig. CHAPTER 9 Point Estimation 9.1 The Rao - Cramér Inequality In Chapter 8 , we used the problem of point estimation of a param- eter to motivate the study of sufficient statistics . In that chapter we ...
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A₁ A₂ accept accordance Accordingly alternative approximately assume called cent Chapter complete compute Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given H₁ Hence hypothesis inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics parameter probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁