## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 61

Page 53

Let X, and Y = XI + X2 have chi-square distributions with ri and r degrees of

freedom,

r — ri degrees of freedom. Hint: Write My(t) = E[e”)] and make use of the

stochastic ...

Let X, and Y = XI + X2 have chi-square distributions with ri and r degrees of

freedom,

**respectively**. Here ri < r. Show that X2 has a chi-square distribution withr — ri degrees of freedom. Hint: Write My(t) = E[e”)] and make use of the

stochastic ...

Page 130

Next let X and Y denote stochastically independent random variables having

normal distributions n(z; ul, alo) and n(y; us, go”),

parameters ul, u2, oi", a 2° are unknown, but at the moment we have no concern

with ul and ...

Next let X and Y denote stochastically independent random variables having

normal distributions n(z; ul, alo) and n(y; us, go”),

**respectively**. The fourparameters ul, u2, oi", a 2° are unknown, but at the moment we have no concern

with ul and ...

Page 133

Denote the means of the samples by X and Y and the variances of the samples

by Si” and So,

mutually stochastically independent. Now X and Y are normally and

stochastically ...

Denote the means of the samples by X and Y and the variances of the samples

by Si” and So,

**respectively**. As was noted on page 130, these four statistics aremutually stochastically independent. Now X and Y are normally and

stochastically ...

### 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