## Introduction to mathematical statistics |

### From inside the book

Results 1-3 of 84

Page 142

4.45. Let X1 and X2 be stochastically independent random variables. Let X1 and

Y = X1 + X2 have chi-square distributions with r1 and r degrees of freedom

degrees ...

4.45. Let X1 and X2 be stochastically independent random variables. Let X1 and

Y = X1 + X2 have chi-square distributions with r1 and r degrees of freedom

**respectively**. Here r1 < r. Show that X2 has a chi-square distribution with r —degrees ...

Page 148

The mean and the variance of the linear function Y = i ktXi 1 are

= 2 k,pf 1 and n aY = 2 kfaf + 2 22 hhPiPPi- 1 i<i The following corollary of this

theorem is quite useful. Corollary. Let X1, . . . , Xn denote the items of a random ...

The mean and the variance of the linear function Y = i ktXi 1 are

**respectively**n py= 2 k,pf 1 and n aY = 2 kfaf + 2 22 hhPiPPi- 1 i<i The following corollary of this

theorem is quite useful. Corollary. Let X1, . . . , Xn denote the items of a random ...

Page 302

If H0 is true, Table II, with k -1=6-1 = i 5 degrees of freedom, shows that we have

Pr (Q6 > 11.1) = 0.05. Now suppose the experimental frequencies of A1,A2,...,A6

are

If H0 is true, Table II, with k -1=6-1 = i 5 degrees of freedom, shows that we have

Pr (Q6 > 11.1) = 0.05. Now suppose the experimental frequencies of A1,A2,...,A6

are

**respectively**13, 19, 11, 8, 5, and 4. The observed value of Q5 is (13 - 10)2 ...### 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 Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere