## 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 270

This reliance is reflected by calling the known interval (x — 2a\sjn, x + 2a/yfn) a

95.4

coefficiehtTTfie'cdnfidence coefficient is equal to the probability IKaYtHe random

...

This reliance is reflected by calling the known interval (x — 2a\sjn, x + 2a/yfn) a

95.4

**percent confidence interval**for p. The number 0.954 is called the confidencecoefficiehtTTfie'cdnfidence coefficient is equal to the probability IKaYtHe random

...

Page 274

Using the fact that the sample mean of the observations, X, is approximately N(n,

a2/n), we see that the interval given by3cą 1.96(15/^) will serve as an

approximate 95

, yfn ...

Using the fact that the sample mean of the observations, X, is approximately N(n,

a2/n), we see that the interval given by3cą 1.96(15/^) will serve as an

approximate 95

**percent confidence interval**for \i. That is, we want or, equivalently, yfn ...

Page 275

(a) If a is known, find the length of a 95

interval is based on the random variable y/9(X — \i)/a. (b) If a is unknown, find the

expected value of the length of a 95

interval ...

(a) If a is known, find the length of a 95

**percent confidence interval**for /i if thisinterval is based on the random variable y/9(X — \i)/a. (b) If a is unknown, find the

expected value of the length of a 95

**percent confidence interval**for p. if thisinterval ...

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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