## Introduction to Mathematical Statistics |

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Page 128

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

r1 and r2

preceding p.d.f.gi(f). The distribution of this random variable is usually called an F

...

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

r1 and r2

**degrees of freedom**respectively, then - U/r, TV/r, has the immediatelypreceding p.d.f.gi(f). The distribution of this random variable is usually called an F

...

Page 313

has an F distribution with b – 1 and (a – 1)(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 2 ...

has an F distribution with b – 1 and (a – 1)(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 2 ...

Page 334

Thus Q/o” has a chisquare distribution with n

random variables Vn(3 – 2)/a and JS (c. – ) (? – B)/o has a normal distribution

with zero mean and unit variance; thus each of Q1/a" and Q2/0% has a chi-

square ...

Thus Q/o” has a chisquare distribution with n

**degrees of freedom**. Each of therandom variables Vn(3 – 2)/a and JS (c. – ) (? – B)/o has a normal distribution

with zero mean and unit variance; thus each of Q1/a" and Q2/0% has a chi-

square ...

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere