## Introduction to mathematical statistics |

### From inside the book

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Page 94

is said to have a

square p.d.f. The mean and the variance of a

(r/2)2 = r and o-2 = ajS2 = (r/2)22 = 2r respectively. For no obvious reason, we ...

is said to have a

**chi**-**square distribution**; and any f(x) of this form is called a chi-square p.d.f. The mean and the variance of a

**chi**-**square distribution**are M = aj8 =(r/2)2 = r and o-2 = ajS2 = (r/2)22 = 2r respectively. For no obvious reason, we ...

Page 312

Qi/a2 has a

= b -2 (Xt. — X)2 > 0. In accordance with the theorem, Q1 and Q2 are

stochastically independent, and Q2/a2 has a

— a(b — 1) ...

Qi/a2 has a

**chi**-**square distribution**with a (b — 1) degrees of freedom. Now a Q2= b -2 (Xt. — X)2 > 0. In accordance with the theorem, Q1 and Q2 are

stochastically independent, and Q2/a2 has a

**chi**-**square distribution**with ab — 1— a(b — 1) ...

Page 379

Index Analysis of variance, 320, 326 Approximate

300 normal for binomial, 199 normal for

of X, 196, 198 Poisson for binomial, 194 Bayes' formula, 54 Bayesian statistics,

164 ...

Index Analysis of variance, 320, 326 Approximate

**distribution**(s),**chi**-**square**,300 normal for binomial, 199 normal for

**chi**-**square**, 194 normal for Poisson, 195of X, 196, 198 Poisson for binomial, 194 Bayes' formula, 54 Bayesian statistics,

164 ...

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### 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