## Introduction to Mathematical Statistics |

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Page 2

For illustration, in Example 2, A might be the collection of every ordered pair of .2/

in which the sum of the pair is

experiment, the outcome is in A, we shall say that the event A has occurred.

For illustration, in Example 2, A might be the collection of every ordered pair of .2/

in which the sum of the pair is

**equal**to seven. If, upon the performance of theexperiment, the outcome is in A, we shall say that the event A has occurred.

Page 10

If A1 = {x; } < r < 3}, A2 = {z; a = }} and As = {z; 0 < r < 10}, find Q(A1), Q(A2), and Q

(Aa). s 1.9. For every one-dimensional set A, let Q(A) be

points in A that correspond to positive integers. If A1 = {r; a a multiple of 3, less ...

If A1 = {x; } < r < 3}, A2 = {z; a = }} and As = {z; 0 < r < 10}, find Q(A1), Q(A2), and Q

(Aa). s 1.9. For every one-dimensional set A, let Q(A) be

**equal**to the number ofpoints in A that correspond to positive integers. If A1 = {r; a a multiple of 3, less ...

Page 352

Prove that each of the nonzero characteristic numbers of A is

only if A* = A. Hint. Let L be an orthogonal matrix such that L'AL = diag|al, a2, ..., a

, and note that A is idempotent if and only if L'AL is idempotent. 13.8. The sum of ...

Prove that each of the nonzero characteristic numbers of A is

**equal**to one if andonly if A* = A. Hint. Let L be an orthogonal matrix such that L'AL = diag|al, a2, ..., a

, and note that A is idempotent if and only if L'AL is idempotent. 13.8. The sum of ...

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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