Introduction to Mathematical Statistics |
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Page 42
... marginal p.d.f. of X1 . In like manner f2 ( x2 ) = √® f ( x1 , x2 ) dxı S = Σf ( x1 , x2 ) 21 is called the marginal p.d.f. of X2 . ( continuous case ) , ( discrete case ) , In some instances we find that ƒ ( X1 , X2 ) = ƒ1 ( X1 ) ƒ2 ...
... marginal p.d.f. of X1 . In like manner f2 ( x2 ) = √® f ( x1 , x2 ) dxı S = Σf ( x1 , x2 ) 21 is called the marginal p.d.f. of X2 . ( continuous case ) , ( discrete case ) , In some instances we find that ƒ ( X1 , X2 ) = ƒ1 ( X1 ) ƒ2 ...
Page 94
... marginal probability density functions . If f1 ( x1 ) > 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the ... marginal p.d.f. fi ( xi ) , provided fi ( x ; ) > 0. We remark that there are many other condi- tional probability density ...
... marginal probability density functions . If f1 ( x1 ) > 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the ... marginal p.d.f. fi ( xi ) , provided fi ( x ; ) > 0. We remark that there are many other condi- tional probability density ...
Page 218
... marginal distributions of U and V make it clear that X has a marginal distribution that is n ( x ; μμ1 , σ12 ) , and that Y has a marginal distribution that is n ( y ; μ2 , σ22 ) . It will now be shown that the number p is actually the ...
... marginal distributions of U and V make it clear that X has a marginal distribution that is n ( x ; μμ1 , σ12 ) , and that Y has a marginal distribution that is n ( y ; μ2 , σ22 ) . It will now be shown that the number p is actually the ...
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