## Introduction to mathematical statistics |

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Page 128

Accordingly, if {7 and V are stochastically independent chi-square variables with

r1 and r2

preceding p.d.f. g^f). The distribution of this random variable is usually called an

F ...

Accordingly, if {7 and V are stochastically independent chi-square variables with

r1 and r2

**degrees of freedom**respectively, then V/r2 has the immediatelypreceding p.d.f. g^f). The distribution of this random variable is usually called an

F ...

Page 312

Qi/a2 has a chi-square distribution with a (b — 1)

= 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) ...

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 313

has an F distribution with b — 1 and (a — l)(b — 1)

subsequent sections it will be seen that some likelihood ratio tests of certain

statistical hypotheses can be based on these F statistics. EXERCISES 12.1. In

Example ...

has an F distribution with b — 1 and (a — l)(b — 1)

**degrees of freedom**. In thesubsequent sections it will be seen that some likelihood ratio tests of certain

statistical hypotheses can be based on these F statistics. EXERCISES 12.1. In

Example ...

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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