## 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 321

X„ is a sufficient

incorrectly the factorization theorem in those instances in which the domain of

positive probability density depends upon the parameter 9. This is due to the fact

that ...

X„ is a sufficient

**statistic for 9**. There is a tendency for some readers to applyincorrectly the factorization theorem in those instances in which the domain of

positive probability density depends upon the parameter 9. This is due to the fact

that ...

Page 322

Show that the sum of the observations of a random sample of size n from a

gamma distribution that has p.d.f. f(x; 9) = (\/9)e~xie, 0 < x < oo, 0 < 9 < oo, zero

elsewhere, is a sufficient

sample of ...

Show that the sum of the observations of a random sample of size n from a

gamma distribution that has p.d.f. f(x; 9) = (\/9)e~xie, 0 < x < oo, 0 < 9 < oo, zero

elsewhere, is a sufficient

**statistic for 9**. 7.15. Let Xu X2, . . . , X„ be a randomsample of ...

Page 352

This is true and in the next section we show that they are independent

EXERCISES 7.53. Let Xu X2, . . . , X„ be a random sample from each of the

following distributions involving the parameter

and ...

This is true and in the next section we show that they are independent

**statistics**.EXERCISES 7.53. Let Xu X2, . . . , X„ be a random sample from each of the

following distributions involving the parameter

**9**. In each case find the m.l.e. of**9**and ...

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### Common terms and phrases

Accordingly approximate best critical region 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 F-distribution gamma distribution given H0 is true hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu percent confidence interval 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 sufficient statistic testing H0 theorem unbiased estimator variance a2 Xx and X2 Yu Y2 zero elsewhere