## 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 146

If this decision is made, only an example in

be skipped because the bivariate normal distribution would not be known. Many

statisticians, however, find it easier to remember the multivariate (including the ...

If this decision is made, only an example in

**Section**4.7 and a few exercises needbe skipped because the bivariate normal distribution would not be known. Many

statisticians, however, find it easier to remember the multivariate (including the ...

Page 481

It is essential that the reader have the background of the multivariate normal

distribution as given in

i=1,2,...,«, denote independent random variables which are N(ph a]), i = 1,2, ... ,n,

...

It is essential that the reader have the background of the multivariate normal

distribution as given in

**Section**4.10 to understand**Sections**10.8 and 10.9. Let Xhi=1,2,...,«, denote independent random variables which are N(ph a]), i = 1,2, ... ,n,

...

Page 526

This formula provides another method of computing U and it shows that a test of

H0 based on U is equivalent to a test based on T. A generalization of T is

considered in

this ...

This formula provides another method of computing U and it shows that a test of

H0 based on U is equivalent to a test based on T. A generalization of T is

considered in

**Section**11.8. Example 1. With the assumptions and the notation ofthis ...

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Accordingly approximate best critical region bivariate normal distribution chi-square distribution complete sufficient statistic conditional p.d.f. conditional probability confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random depend upon 9 discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters equation estimator of 9 Example Exercise gamma distribution given H0 is true hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 likelihood function limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random sample random variables Xx reject H0 respectively sample space Section Show significance level simple hypothesis statistic for 9 testing H0 theorem u(Xu X2 unbiased estimator variance a2 XuX2 Xx and X2 Yu Y2 zero elsewhere