## Introduction to Mathematical Statistics |

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Page 18

It is seen that whether the

continuous type, the probability Pr(X e A) is completely determined by a function f

(r). In either case f(x) is called the probability density function (hereafter

abbreviated ...

It is seen that whether the

**random variable**X is of the discrete type or of thecontinuous type, the probability Pr(X e A) is completely determined by a function f

(r). In either case f(x) is called the probability density function (hereafter

abbreviated ...

Page 108

n In accordance with this definition, the

above is a statistic. But the

unless p and q are known numbers. It should be noted that, although a statistic

does not ...

n In accordance with this definition, the

**random variable**Y = X. X, 1 discussedabove is a statistic. But the

**random variable**Y = (X1 — p.)/o is not a statisticunless p and q are known numbers. It should be noted that, although a statistic

does not ...

Page 320

309, is valid regardless of whether the

chi-square variables. We next discuss a noncentral F variable. If U and V are

stochastically independent and are respectively x*(ru) and x*(r2), the random ...

309, is valid regardless of whether the

**random variables**are central or noncentralchi-square variables. We next discuss a noncentral F variable. If U and V are

stochastically independent and are respectively x*(ru) and x*(r2), the random ...

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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