## 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 231

Two independent random samples, each of size 6, are taken from two normal

distributions having common variance a2. ... The mean and variance of 9

observations are 4 and 14, respectively. ... from a

variance a2.

Two independent random samples, each of size 6, are taken from two normal

distributions having common variance a2. ... The mean and variance of 9

observations are 4 and 14, respectively. ... from a

**distribution with mean**\i andvariance a2.

Page 244

Let Y„ have a

same for every n; that is, p = n/n, where \i is a constant. We shall find the limiting

Let Y„ have a

**distribution**that is b(n, p). Suppose that the**mean**p. = np is thesame for every n; that is, p = n/n, where \i 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).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„ — r^lsfn isnormal with

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

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### Common terms and phrases

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