## 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 13

Finally, we observe from the following

is in the collection, its complement must be one of those subsets. In particular, the

null set, which is the complement of c€, must be in the collection. The following ...

Finally, we observe from the following

**theorems**and their proofs that if the set Cis in the collection, its complement must be one of those subsets. In particular, the

null set, which is the complement of c€, must be in the collection. The following ...

Page 247

In probability theory there is a very elegant

that if Xu X2, . . . ,X„ denote the observations of a random sample of size n from

any ...

In probability theory there is a very elegant

**theorem**called the central limit**theorem**. A special case of this**theorem**asserts the remarkable and important factthat if Xu X2, . . . ,X„ denote the observations of a random sample of size n from

any ...

Page 255

Then, by

accordance with

...

Then, by

**Theorem**4, (K„/«)(1 — Y„/n)/[p(\ — p)] converges in probability to 1, and**Theorem**5 asserts that the following does also: (YJn)(\ - YJrif pO-p) Thus, inaccordance with

**Theorem**6, the ratio W„ = U„/V„, namely y„ ~ np Jn{Y„\n){\ - YJn)'...

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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