Introduction to Mathematical Statistics |
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Page 58
... interval [ Ẵ – ( 20 / √√ñ ) , Ẵ + ( 20 / n ) ] is called a random interval : that is , an interval at least one of whose endpoints is a random variable . In this case both end points of the interval are random variables ( here ...
... interval [ Ẵ – ( 20 / √√ñ ) , Ẵ + ( 20 / n ) ] is called a random interval : that is , an interval at least one of whose endpoints is a random variable . In this case both end points of the interval are random variables ( here ...
Page 59
... interval either does or does not include μ . However , the fact that we had such a high degree of probability , prior to the performance of the experiment , that the random interval [ X – ( 20 / √ñ ) , Ẵ + ( 20 / √n ) ] includes the ...
... interval either does or does not include μ . However , the fact that we had such a high degree of probability , prior to the performance of the experiment , that the random interval [ X – ( 20 / √ñ ) , Ẵ + ( 20 / √n ) ] includes the ...
Page 61
... interval ( Xi b - μ ) 2 n ( Xi α - μ ) 2 is a 95 per cent confidence ... random sample from a distribution that is n ( x ; μ , σ2 ) . Theorem 2 of ... random variables , each having a chi - square distribution with one degree of freedom ...
... interval ( Xi b - μ ) 2 n ( Xi α - μ ) 2 is a 95 per cent confidence ... random sample from a distribution that is n ( x ; μ , σ2 ) . Theorem 2 of ... random variables , each having a chi - square distribution with one degree of freedom ...
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