Introduction to Mathematical Statistics |
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Page 96
... statistic X = ( X + X2 + X2 ... + X9 ) / 9 is normal with mean • and variance 2 1/9 . Thus is an unbiased statistic for 0. The statistic X1 is also normal with mean 0 and variance σx , 2 = 1 = X 1 1 ; so X1 is also an unbiased statistic ...
... statistic X = ( X + X2 + X2 ... + X9 ) / 9 is normal with mean • and variance 2 1/9 . Thus is an unbiased statistic for 0. The statistic X1 is also normal with mean 0 and variance σx , 2 = 1 = X 1 1 ; so X1 is also an unbiased statistic ...
Page 104
... statistic for 0 . 5.14 . Let X1 , X2 , ... Xn be a random sample from the normal distribution n n ( x ; 0 , 0 ) , 0 < 0 < ∞ . Show that X , is a sufficient statistic ... unbiased statistic for 0 ; that is , E ( Y2 ) = 0. Let the joint p.d.f. ...
... statistic for 0 . 5.14 . Let X1 , X2 , ... Xn be a random sample from the normal distribution n n ( x ; 0 , 0 ) , 0 < 0 < ∞ . Show that X , is a sufficient statistic ... unbiased statistic for 0 ; that is , E ( Y2 ) = 0. Let the joint p.d.f. ...
Page 106
... unbiased statistic for 0. Then E ( Y21 ) Then E ( Y2y1 ) = ( y1 ) defines a statistic ( Y1 ) . This statistic ( Y1 ) is a function of the sufficient statistic for 0 ; it is an unbiased statistic for 0 ; and its variance is less than ...
... unbiased statistic for 0. Then E ( Y21 ) Then E ( Y2y1 ) = ( y1 ) defines a statistic ( Y1 ) . This statistic ( Y1 ) is a function of the sufficient statistic for 0 ; it is an unbiased statistic for 0 ; and its variance is less than ...
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