Introduction to Mathematical Statistics |
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Page 22
... moment - generating function of X ( or of the distribution ) and is denoted by Mx ( t ) . That is , Mx ( t ) = E ( ex ) . It is evident that if we set t = 0 , we have Mx ( 0 ) = 1. As will be seen by example , not every distribution has a ...
... moment - generating function of X ( or of the distribution ) and is denoted by Mx ( t ) . That is , Mx ( t ) = E ( ex ) . It is evident that if we set t = 0 , we have Mx ( 0 ) = 1. As will be seen by example , not every distribution has a ...
Page 25
... moment - generating function of this distribution , if it exists , is given by Mx ( t ) = - E ( etX ) = Σetzf ( x ) ∞6etx Σ π2x2 The ratio test may be used to show that this series converges only if t≤0 . Thus there does not exist a ...
... moment - generating function of this distribution , if it exists , is given by Mx ( t ) = - E ( etX ) = Σetzf ( x ) ∞6etx Σ π2x2 The ratio test may be used to show that this series converges only if t≤0 . Thus there does not exist a ...
Page 143
... moment - generating function of Y in the form My ( t ; n ) . The following theorem , which is essentially Curtiss ' modification of a theorem of Lévy and Cramér , explains how the moment - generating func- tion may be used in problems ...
... moment - generating function of Y in the form My ( t ; n ) . The following theorem , which is essentially Curtiss ' modification of a theorem of Lévy and Cramér , explains how the moment - generating func- tion may be used in problems ...
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