## 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 91

Page 41

Our notation can be considerably simplified when we restrict ourselves to random

variables of the continuous or discrete types. Suppose that the space of a

e~x, ...

Our notation can be considerably simplified when we restrict ourselves to random

variables of the continuous or discrete types. Suppose that the space of a

**continuous type**of random variable X is «s/ = {X:0<X<oo} and that the p.d.f. of X ise~x, ...

Page 45

for the discrete type of random variable, and F{x) = f(w)dw, •'-00 for the

being of the continuous or discrete type, depending on whether the random

variable is of the ...

for the discrete type of random variable, and F{x) = f(w)dw, •'-00 for the

**continuous type**of random variable. We speak of a distribution function F(x) asbeing of the continuous or discrete type, depending on whether the random

variable is of the ...

Page 84

That is,/2|i(-^2ki) has the properties of a p.d.f. of one

variable. It is called the conditional p.d.f. of the

variable X2, given that the

.

That is,/2|i(-^2ki) has the properties of a p.d.f. of one

**continuous type**of randomvariable. It is called the conditional p.d.f. of the

**continuous type**of randomvariable X2, given that the

**continuous type**of random variable Xx has the value x,.

### 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 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