Introduction to Mathematical Statistics |
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Page 46
... mutually stochastically independent if , and only if , f ( x1 , x2 , ... , Xn ) = ƒ1 ( X1 ) ƒ2 ( X2 ) ··· fn ( n ) ... stochastically independent random variables X1 and X2 becomes , for mutually sto- chastically independent random ...
... mutually stochastically independent if , and only if , f ( x1 , x2 , ... , Xn ) = ƒ1 ( X1 ) ƒ2 ( X2 ) ··· fn ( n ) ... stochastically independent random variables X1 and X2 becomes , for mutually sto- chastically independent random ...
Page 52
... mutually stochastically independent . Now SO Thus as stated . E ( e1X ) = Mx , ( t ) ; E ( etkiXi ) = Mx , ( kit ) . n My ( t ) = [ [ Mx , ( k 、 t ) i = 1 Some very useful results are obtained if we make the following modification in ...
... mutually stochastically independent . Now SO Thus as stated . E ( e1X ) = Mx , ( t ) ; E ( etkiXi ) = Mx , ( kit ) . n My ( t ) = [ [ Mx , ( k 、 t ) i = 1 Some very useful results are obtained if we make the following modification in ...
Page 53
... stochastic independence of X1 and X2 . - = ... 3.13 . Let Y be the sum of n mutually stochastically independent chi - square variables X1 , X2 , ... , Xn with r1 , T2 , ... , 7 degrees of freedom , respectively . Show that Y has a chi ...
... stochastic independence of X1 and X2 . - = ... 3.13 . Let Y be the sum of n mutually stochastically independent chi - square variables X1 , X2 , ... , Xn with r1 , T2 , ... , 7 degrees of freedom , respectively . Show that Y has a chi ...
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