Introduction to Mathematical Statistics |
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Page 57
... normal distribution n ( x ; 6 , 4 ) . Determine the probability that the largest sample item exceeds 8 . 3.27 . Show that the moment - generating function of the sum Y of the items of a random sample of size n from a distribution having ...
... normal distribution n ( x ; 6 , 4 ) . Determine the probability that the largest sample item exceeds 8 . 3.27 . Show that the moment - generating function of the sum Y of the items of a random sample of size n from a distribution having ...
Page 132
... normal distributions n ( x ; μ1 , σ12 ) and n ( y ; μ2 , σ22 ) , respec- tively , yield 13.6 , 822 = 7.26 . Find a ... distribution , provided the variance was known . It will now be shown that this statistical inference can be made even ...
... normal distributions n ( x ; μ1 , σ12 ) and n ( y ; μ2 , σ22 ) , respec- tively , yield 13.6 , 822 = 7.26 . Find a ... distribution , provided the variance was known . It will now be shown that this statistical inference can be made even ...
Page 219
... where q = 1 ∞ Son S ( x — μ1 ) 2 012 - Chattay - 1 2πσισε 1/1 - ρε ― ( x — μ1 ) ( Y — μ2 ) 2p ( 20 0102 ( u + 2 * dx dy - M2 ) 2 022 Without the use of the algebra of matrices , it $ 11.2 ] 219 THE BIVARIATE NORMAL DISTRIBUTION.
... where q = 1 ∞ Son S ( x — μ1 ) 2 012 - Chattay - 1 2πσισε 1/1 - ρε ― ( x — μ1 ) ( Y — μ2 ) 2p ( 20 0102 ( u + 2 * dx dy - M2 ) 2 022 Without the use of the algebra of matrices , it $ 11.2 ] 219 THE BIVARIATE NORMAL DISTRIBUTION.
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