Introduction to Mathematical Statistics |
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Page 52
... My ( t ) is as given in relation ( iii ) follows from as stated in relation ( ii ) . My ( t ) == E [ e “ ( k2X1 + k2Xs + ••• + kaXn ) ] = E ( e1kıX1 ) E ( etkaXs ) ... E ( etkaX * ) , since X1 , X2 , ... , Xn are mutually stochastically ...
... My ( t ) is as given in relation ( iii ) follows from as stated in relation ( ii ) . My ( t ) == E [ e “ ( k2X1 + k2Xs + ••• + kaXn ) ] = E ( e1kıX1 ) E ( etkaXs ) ... E ( etkaX * ) , since X1 , X2 , ... , Xn are mutually stochastically ...
Page 143
... My ( t ; n ) . The following theorem , which is essentially Curtiss ' modification of a theorem of Lévy and Cramér ... My ( t ; n ) that exists for -h < t < h for all n . If there exists a distribution function F ( y ) , with ...
... My ( t ; n ) . The following theorem , which is essentially Curtiss ' modification of a theorem of Lévy and Cramér ... My ( t ; n ) that exists for -h < t < h for all n . If there exists a distribution function F ( y ) , with ...
Page 147
... ( t ) = = 1 + [ m ' ' ( § ) — σ2 ] t2 - + 2 2 as was to be shown . Next consider My ( t ; n ) where In m ( t ) , 1 My ( t ; n ) ELe o√n = t ( X1 - μ ) t ( X , —μ ) t ( Xn - μ ) = E [ e TM . Be one on .... t o√n = £ [ e ° √ ñ3 · ~ * ) ...
... ( t ) = = 1 + [ m ' ' ( § ) — σ2 ] t2 - + 2 2 as was to be shown . Next consider My ( t ; n ) where In m ( t ) , 1 My ( t ; n ) ELe o√n = t ( X1 - μ ) t ( X , —μ ) t ( Xn - μ ) = E [ e TM . Be one on .... t o√n = £ [ e ° √ ñ3 · ~ * ) ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²