## Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |

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Page 239

If we knew more about the gamma function, it is easy to show that the first

also equals 1 . Thus we have and hence T„ has a

n from ...

If we knew more about the gamma function, it is easy to show that the first

**limit**also equals 1 . Thus we have and hence T„ has a

**limiting**standard normal**distribution**. EXERCISES 5.1. Let X„ denote the mean of a random sample of sizen from ...

Page 243

5.3 Limiting Moment-Generating Functions To find the

function of a random variable Y„ by use of the definition of

function obviously requires that we know F„(y) for each positive integer n. But, as

indicated ...

5.3 Limiting Moment-Generating Functions To find the

**limiting distribution**function of a random variable Y„ by use of the definition of

**limiting distribution**function obviously requires that we know F„(y) for each positive integer n. But, as

indicated ...

Page 244

Accordingly, for every fixed value of /, the limit is e'2'2. Example 1. Let Y„ have a

distribution that is />). Suppose that the mean \i = np is the same for every n; that

is, /7 = n/n, where is a constant. We shall find the

Accordingly, for every fixed value of /, the limit is e'2'2. Example 1. Let Y„ have a

distribution that is />). Suppose that the mean \i = np is the same for every n; that

is, /7 = n/n, where is a constant. We shall find the

**limiting distribution**of the ...### What people are saying - Write a review

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