## Introduction to Mathematical Statistics |

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Page 343

This investigation assumes that the student is familiar with elementary

algebra, with real

. Henceforth the expression quadratic form means a quadratic form in a

prescribed ...

This investigation assumes that the student is familiar with elementary

**matrix**algebra, with real

**symmetric**quadratic forms, and with orthogonal transformations. Henceforth the expression quadratic form means a quadratic form in a

prescribed ...

Page 352

Find the moment-generating function of Q/g”. 13.7. Let A be a real

if and only if A* = A. Hint. Let L be an orthogonal matrix such that L'AL = diag|al,

a2, ...

Find the moment-generating function of Q/g”. 13.7. Let A be a real

**symmetric****matrix**. Prove that each of the nonzero characteristic numbers of A is equal to oneif and only if A* = A. Hint. Let L be an orthogonal matrix such that L'AL = diag|al,

a2, ...

Page 358

Let Y = X at Xi, where a1, a2, a3, and as are 1 real constants. If Yo and Q = X1X2

– XaX, are stochastically independent, determine ai, a2, as, and a1. 13.13. Let A

be the real

Let Y = X at Xi, where a1, a2, a3, and as are 1 real constants. If Yo and Q = X1X2

– XaX, are stochastically independent, determine ai, a2, as, and a1. 13.13. Let A

be the real

**symmetric matrix**of a quadratic form Q in the items of a random ...### What people are saying - Write a review

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### Common terms and phrases

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