Introduction to Mathematical Statistics |
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Page 63
... accordance with y = 4x . We note two things about this transformation : It is such that to each point in A there corresponds one , and only one , point in B ; and conversely , to each point in B there corresponds one , and only one ...
... accordance with y = 4x . We note two things about this transformation : It is such that to each point in A there corresponds one , and only one , point in B ; and conversely , to each point in B there corresponds one , and only one ...
Page 144
... accordance with the theorem and under the conditions stated , it is seen that Y has a limiting Poisson distribution with mean μ . Whenever a random variable has a limiting distribution , we may , if we wish , use the limiting ...
... accordance with the theorem and under the conditions stated , it is seen that Y has a limiting Poisson distribution with mean μ . Whenever a random variable has a limiting distribution , we may , if we wish , use the limiting ...
Page 188
... accordance with page 134 , a t distribution with n + m freedom . Thus the random variable defined by λ2 / ( n + m ) is n + m - - 2 ( n + m − 2 ) + T2 - - 2 degrees of The test of Ho against all alternatives may then be based on a t ...
... accordance with page 134 , a t distribution with n + m freedom . Thus the random variable defined by λ2 / ( n + m ) is n + m - - 2 ( n + m − 2 ) + T2 - - 2 degrees of The test of Ho against all alternatives may then be based on a t ...
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