## 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 244

Let Y„ have a

every n; that is, /7 = n/n, where is a constant. We shall find the limiting

of the binomial

Let Y„ have a

**distribution**that is />). Suppose that the**mean**\i = np is the same forevery n; that is, /7 = n/n, where is a constant. We shall find the limiting

**distribution**of the binomial

**distribution**, when p = n/n, by finding the limit of M(t; n). Now M(t ...Page 246

Let the random variable Z„ have a Poisson

Show that the limiting

normal with

random ...

Let the random variable Z„ have a Poisson

**distribution**with parameter n — n.Show that the limiting

**distribution**of the random variable Y„ = (Z„ — n)/y/n isnormal with

**mean**zero and variance 1. 5.16. Let S2„ denote the variance of arandom ...

Page 257

observations of a random sample of size 24 from a chi-square

degrees of freedom is between 70 and 80. ... It can be proved that the

a random sample of size n from a Cauchy

observations of a random sample of size 24 from a chi-square

**distribution**with 3degrees of freedom is between 70 and 80. ... It can be proved that the

**mean**X„ ofa random sample of size n from a Cauchy

**distribution**has that same Cauchy ...### What people are saying - Write a review

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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