## Introduction to Mathematical Statistics |

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Page 318

F = 12.3

stochastically independent random variables that are n(pot, a”), i = 1, 2, ..., n and

let Y = $ X#/go. If each put is zero, we know that Y is x*(n). We shall now 1

investigate ...

F = 12.3

**Noncentral**X” and**Noncentral**F Let X1, X2,..., Xn denote mutuallystochastically independent random variables that are n(pot, a”), i = 1, 2, ..., n and

let Y = $ X#/go. If each put is zero, we know that Y is x*(n). We shall now 1

investigate ...

Page 320

no fortuitous circumstance; any quadratic form Q = Q(X1, ..., Xn) in normally

distributed variables, which is such that Q/o” is x*(r, 6), has 6 = Q(ul, u2, ..., un)/o”;

and if Q/o” is a chi-square variable (central or

of pu ...

no fortuitous circumstance; any quadratic form Q = Q(X1, ..., Xn) in normally

distributed variables, which is such that Q/o” is x*(r, 6), has 6 = Q(ul, u2, ..., un)/o”;

and if Q/o” is a chi-square variable (central or

**noncentral**) for certain real valuesof pu ...

Page 381

... 52, 53 Multivariate normal distribution, see Distribution Neyman-Pearson

theorem, 262, 279, 282,293

, see Distribution

Distribution ...

... 52, 53 Multivariate normal distribution, see Distribution Neyman-Pearson

theorem, 262, 279, 282,293

**Noncentral**chi-square, see Distribution**Noncentral**F, see Distribution

**Noncentral**parameter, 292, 319, 320**Noncentral**T, seeDistribution ...

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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