## 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 30

Page 209

Robert V. Hogg. then the

, . . . ,ak are real constants, is MAO = fl M,(a,t). /= i Proof. The

M Y(t) = E[etY] = E[et(a* Xl +"2X2+ □□ + a„X„)] = E[ea* tX^eaitXl . . □ ea"tX„] ...

Robert V. Hogg. then the

**moment**-**generating function**of. Y= taM,. /= i where aua2, . . . ,ak are real constants, is MAO = fl M,(a,t). /= i Proof. The

**m.g.f.**of Y is given byM Y(t) = E[etY] = E[et(a* Xl +"2X2+ □□ + a„X„)] = E[ea* tX^eaitXl . . □ ea"tX„] ...

Page 213

Let Xu X2 be two independent gamma random variables with parameters a\ = 3,

/?, = 3 and a2 = 5, j82 = L respectively. (a) Find the

What is the distribution of Yl 4.82. A certain job is completed in three steps in

series.

Let Xu X2 be two independent gamma random variables with parameters a\ = 3,

/?, = 3 and a2 = 5, j82 = L respectively. (a) Find the

**m.g.f.**of F = 2*, + 6AV (b)What is the distribution of Yl 4.82. A certain job is completed in three steps in

series.

Page 243

5.3 Limiting

function of a random variable Y„ by use of the definition of limiting distribution

function obviously requires that we know F„(y) for each positive integer n. But, as

indicated ...

5.3 Limiting

**Moment**-**Generating Functions**To find the limiting distributionfunction of a random variable Y„ by use of the definition of limiting distribution

function obviously requires that we know F„(y) for each positive integer n. But, as

indicated ...

### 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