## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 85

Page 69

First the product of two nonnegative functions f(

positive on a product space. That is, if f(

on, the respective spaces &1 and sya, then the product of fi (21) and f2(

First the product of two nonnegative functions f(

**x1**)f,(r2) means a function that ispositive on a product space. That is, if f(

**x1**) and f2(**x2**) are positive on, and onlyon, the respective spaces &1 and sya, then the product of fi (21) and f2(

**x2**) is ...Page 70

If

x1) and f2(x2) are the marginal probability density functions of

respectively. Thus, the condition f(

If

**X1 and X2**are stochastically independent, then f(**x1**,**x2**) = fi(x1)fa(z2), where fi(x1) and f2(x2) are the marginal probability density functions of

**X1 and X2**respectively. Thus, the condition f(

**x1**,**x2**) = g(xi)h(x2) is fulfilled. Conversely, if f(**x1**,**x2**) ...Page 72

Let the stochastically independent random variables X, and

probability density functions f(

the product of a function u(XI) of

Let the stochastically independent random variables X, and

**X2**have the marginalprobability density functions f(

**x1**) and fa(**x2**) respectively. The expected value ofthe product of a function u(XI) of

**X1**alone and a function v(**X2**) of**X2**alone is, ...### 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

accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere