## Introduction to Mathematical Statistics |

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Page 343

This investigation assumes that the student is familiar with elementary

algebra, with real symmetric quadratic forms, and with orthogonal transformations

. 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 348

Let X1, X2,.. .., X, have a multivariate normal distribution, where p is the

the means and V is the positive definite covariance

, where X = [X1, ..., Xn], c' = [c1, ..., ca), and d' = [di,..., d.] are real

Let X1, X2,.. .., X, have a multivariate normal distribution, where p is the

**matrix**ofthe means and V is the positive definite covariance

**matrix**. Let Y = c'X and Z = d'X, where X = [X1, ..., Xn], c' = [c1, ..., ca), and d' = [di,..., d.] are real

**matrices**.Page 352

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

if and only if A* = A. Hint. Let L be an orthogonal

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, ...

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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