## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 85

Page 41

In this chapter we shall investigate the distributions of certain functions of one or

more random variables. For example, suppose that f(x1, x2) is the p.d.f. of two

the ...

In this chapter we shall investigate the distributions of certain functions of one or

more random variables. For example, suppose that f(x1, x2) is the p.d.f. of two

**random variables X1**and X2. Then Y = X1 + X2 and Z = X1,X2 are functions ofthe ...

Page 46

The theorem that E[u(X)w(X2)] = E[u(X)]E[v(X2)] for stochastically independent

The theorem that E[u(X)w(X2)] = E[u(X)]E[v(X2)] for stochastically independent

**random variables X1**and X2 becomes, for mutually stochastically independent**random variables X1**, X2, ..., Xn, Esu (XI) u2(X2) ... un(X,)] ...Page 53

Let

X2 have chi-square distributions with ri and r degrees of freedom, respectively.

Here ri < r. Show that X2 has a chi-square distribution with r — ri degrees of ...

Let

**Xi**and X, be stochastically independent**random variables**. 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 with r — ri degrees of ...

### 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