Introduction to Mathematical Statistics |
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Page 94
... joint p.d.f. of the n random variables X1 , X2 , ... , Xn . Let fi ( x1 ) , ƒ2 ( X2 ) , ... , fn ( xn ) be respec ... joint conditional p.d.f. of X2 , ...... , Xn , given X1 = 1. More generally , the joint conditional p.d.f. of any n - 1 ...
... joint p.d.f. of the n random variables X1 , X2 , ... , Xn . Let fi ( x1 ) , ƒ2 ( X2 ) , ... , fn ( xn ) be respec ... joint conditional p.d.f. of X2 , ...... , Xn , given X1 = 1. More generally , the joint conditional p.d.f. of any n - 1 ...
Page 114
... joint p.d.f. of X1 , X2 , X3 ] is called the con- ditional p.d.f. of X4 , ... , Xn , given X1 = X1 , X2 X2 , X3 = X3 . The conditional p.d.f. of any number of the random variables X1 , X2 , *** , given values for the remaining variables ...
... joint p.d.f. of X1 , X2 , X3 ] is called the con- ditional p.d.f. of X4 , ... , Xn , given X1 = X1 , X2 X2 , X3 = X3 . The conditional p.d.f. of any number of the random variables X1 , X2 , *** , given values for the remaining variables ...
Page 118
... joint p.d.f. of these m joint sufficient statistics is complete . Exercises 2 5.29 . Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 from the distribution with p.d.f. 1 02 f ( x ; 01 , 02 ) = -e 1 2 3 ( x - 01 ) ...
... joint p.d.f. of these m joint sufficient statistics is complete . Exercises 2 5.29 . Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 from the distribution with p.d.f. 1 02 f ( x ; 01 , 02 ) = -e 1 2 3 ( x - 01 ) ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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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