## Introduction to Mathematical Statistics |

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Page 179

are mutually stochastically independent and each, in accordance with Theorem 1

, has a uniform distribution on the interval (0, 1). Thus F(X1), F(X2), ..., F(Xa) is a ...

**Consider**the random variables F(X1), F(X2), ..., F(Xa). These random variablesare mutually stochastically independent and each, in accordance with Theorem 1

, has a uniform distribution on the interval (0, 1). Thus F(X1), F(X2), ..., F(Xa) is a ...

Page 310

Let the random variable X have a distribution that is n(pu, oo). Let a and b denote

positive integers greater than one and let n = ab.

size n = ab from this normal distribution. The items of the random sample will be ...

Let the random variable X have a distribution that is n(pu, oo). Let a and b denote

positive integers greater than one and let n = ab.

**Consider**a random sample ofsize n = ab from this normal distribution. The items of the random sample will be ...

Page 330

Show that a likelihood ratio test of Ho against all possible alternatives may be

based, in the notation of Section 12.1, on the F = (b – 1)(Q2/Q3) statistic having (a

– 1) ...

**Consider**the 1 1 hypothesis Ho: put = u + 8, (or Ho: & 1 = 0.2 = . . . = ga = 0).Show that a likelihood ratio test of Ho against all possible alternatives may be

based, in the notation of Section 12.1, on the F = (b – 1)(Q2/Q3) statistic having (a

– 1) ...

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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