Introduction to Mathematical Statistics |
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Page 166
... alternative hypothesis H1 : 0 = 2. There is no limit to the number of rules or tests that can be constructed . We shall compare two such tests , and to keep the exposition simple , the size of the random sample will be taken to be n = 2 ...
... alternative hypothesis H1 : 0 = 2. There is no limit to the number of rules or tests that can be constructed . We shall compare two such tests , and to keep the exposition simple , the size of the random sample will be taken to be n = 2 ...
Page 176
... alternative simple hypothesis H1 : 01 = 0 " 1 = 1 , 02 = 0 " 2 = 4 . 01 9.10 . Let X1 , Xn denote a random sample from a normal distribution n ( x ; 0 , 100 ) . Show that C ′ = { ( X1 , X2 , ··· , Xn ) ; c ≤ x = x ; / n } is a best ...
... alternative simple hypothesis H1 : 01 = 0 " 1 = 1 , 02 = 0 " 2 = 4 . 01 9.10 . Let X1 , Xn denote a random sample from a normal distribution n ( x ; 0 , 100 ) . Show that C ′ = { ( X1 , X2 , ··· , Xn ) ; c ≤ x = x ; / n } is a best ...
Page 182
... alternative composite hypothesis or of constructing a test of a null simple hypothesis against an alternative composite hy- pothesis when a uniformly most powerful test does not exist . This method leads to tests that are called ...
... alternative composite hypothesis or of constructing a test of a null simple hypothesis against an alternative composite hy- pothesis when a uniformly most powerful test does not exist . This method leads to tests that are called ...
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