## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 73

Page 55

Certain functions of the items of a random sample are given a special name, as

indicated by the following definition. Definition 2. Let X1, X2, ..., Xn

function of ...

Certain functions of the items of a random sample are given a special name, as

indicated by the following definition. Definition 2. Let X1, X2, ..., Xn

**denote a****random**sample from a given distribution. Let Y = u(X1, X2, ..., Xn) denote afunction of ...

Page 96

For example, let X1, X2, ..., X,

m(x; 6, 1). In accordance with the theorem of Section 3.3, page 56, the statistic X

= (X, + X, + ... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an ...

For example, let X1, X2, ..., X,

**denote a random**sample from a normal distributionm(x; 6, 1). In accordance with the theorem of Section 3.3, page 56, the statistic X

= (X, + X, + ... + X)/9 is normal with mean 6 and variance or” = 1/9. Thus X is an ...

Page 100

Since we are dealing with random variables of the discrete type, no Jacobian is

involved, and at points of nonzero ... Let X1, X2, X2, X4,

from a distribution having p.d.f. f(x, y = } 0 < x < 0, 0 < 0 < co, = 0 elsewhere.

Since we are dealing with random variables of the discrete type, no Jacobian is

involved, and at points of nonzero ... Let X1, X2, X2, X4,

**denote a random**samplefrom a distribution having p.d.f. f(x, y = } 0 < x < 0, 0 < 0 < co, = 0 elsewhere.

### 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 best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere