Introduction to Mathematical Statistics |
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Page 18
... integral ( or sum ) converge absolutely . However , in this book , each u ( x ) is of such a character that if the integral ( or sum ) exists , the convergence is absolute . Accordingly , we have not burdened the student with this ...
... integral ( or sum ) converge absolutely . However , in this book , each u ( x ) is of such a character that if the integral ( or sum ) exists , the convergence is absolute . Accordingly , we have not burdened the student with this ...
Page 19
... integral ( or the n - fold sum , as the case may be ) is called the mathematical expecta- tion , denoted by E [ u ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
... integral ( or the n - fold sum , as the case may be ) is called the mathematical expecta- tion , denoted by E [ u ... integral ( or sum ) of a constant times a function is the constant times the integral ( or sum ) of the function . Of ...
Page 36
... integral yk - le - udy 0 exists for k > 0 and that the value of the integral is a positive number . The integral is called the gamma function of k and we write If k = 1 , clearly г ( k ) = S 0 yk - le - vdy . r ( 1 ) = √Re- e- " dy = 1 ...
... integral yk - le - udy 0 exists for k > 0 and that the value of the integral is a positive number . The integral is called the gamma function of k and we write If k = 1 , clearly г ( k ) = S 0 yk - le - vdy . r ( 1 ) = √Re- e- " dy = 1 ...
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