## Introduction to Mathematical Statistics |

### From inside the book

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Page 143

The following

Lévy and Cramér, explains how the moment-generating function may be used in

problems of limiting distributions. A proof of the

...

The following

**theorem**, which is essentially Curtiss' modification of a**theorem**ofLévy and Cramér, explains how the moment-generating function may be used in

problems of limiting distributions. A proof of the

**theorem**requires a knowledge of...

Page 146

called the Central Limit

remarkable and important fact that if X1, X2, ..., Xn denote the items of a random

sample of size n from any distribution having finite variance o” (and hence finite

mean ...

called the Central Limit

**Theorem**. A special case of this**theorem**asserts theremarkable and important fact that if X1, X2, ..., Xn denote the items of a random

sample of size n from any distribution having finite variance o” (and hence finite

mean ...

Page 191

Throughout this book the student has been encouraged to accept without proof (

at this time)

in probability and statistics. At this point a

Throughout this book the student has been encouraged to accept without proof (

at this time)

**theorems**in analysis which enable him to prove for himself**theorems**in probability and statistics. At this point a

**theorem**in matrix algebra is helpful.### What people are saying - Write a review

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere