## 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

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

normal distributions having common variance a2. If Wx and W2 are the ... be a

random sample from a

second ...

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

normal distributions having common variance a2. If Wx and W2 are the ... be a

random sample from a

**distribution with mean**\i and variance a2. Consider thesecond ...

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 p = 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 249

approximate normal p.d.f. as though it were the exact p.d.f. of X. Some illustrative

examples, here and later, will help show the importance of this version of the

central ...

**distribution with mean**\i and variance a2/n; and in applications we use theapproximate normal p.d.f. as though it were the exact p.d.f. of X. Some illustrative

examples, here and later, will help show the importance of this version of the

central ...

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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 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 Yx 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 statistic for 9 subset testing H0 theorem u(Xu X2 unbiased estimator XuX2 Xx and X2 Yu Y2 zero elsewhere