## 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. |

### From inside the book

Results 1-3 of 83

Page 220

Theorem 5. Let Xu . . . , X„ denote random variables that have means fiu . . . , fi„

and

Xj and let ku...,k„ denote real constants. The mean and the

Theorem 5. Let Xu . . . , X„ denote random variables that have means fiu . . . , fi„

and

**variances**a\, . . . ,**a2**„. Let pu, i ^j, denote the correlation coefficient of X> andXj and let ku...,k„ denote real constants. The mean and the

**variance**of the linear ...Page 222

Let Xu X2, . . . , X„ be a random sample of size n from a distribution with mean n

and

random sample. Hint: Write S2 = (1/«) £ (*, - /*)2 - (^ - //)2. i 4.118. Let A"| and Z2 ...

Let Xu X2, . . . , X„ be a random sample of size n from a distribution with mean n

and

**variance a2**. Show that E(S2) = (« — 1)ff2/«, where S2 is the variance of therandom sample. Hint: Write S2 = (1/«) £ (*, - /*)2 - (^ - //)2. i 4.118. Let A"| and Z2 ...

Page 277

Thus X and Y are normally and independently distributed with means fix and n2

and

difference X — Y is normally distributed with mean p\ — P2 and

...

Thus X and Y are normally and independently distributed with means fix and n2

and

**variances a2**/n and q^/m,_respectively. In accordance with Section 4.7, theirdifference X — Y is normally distributed with mean p\ — P2 and

**variance a2**In +...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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