## Introduction to Mathematical Statistics |

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Page 12

1 = 0, and the

that ...

**Theorem**2. The probability of the null set is zero, that is, P(0) = 0. Proof. In**Theorem**1, take A = 0 so that A* = .9/. Accordingly, we have P(0) = 1 — P(y) = 1 –1 = 0, and the

**theorem**is proved.**Theorem**3. If A1 and A2 are subsets of .2/ suchthat ...

Page 196

This exercise and the immediately preceding one are special instances of an

important

normal ...

This exercise and the immediately preceding one are special instances of an

important

**theorem**that will be proved in the next section. 7.4 The Central Limit**Theorem**It was seen, p. 144, that, if X1, X2,..., Xn is a random sample from anormal ...

Page 355

Since the moment-generating function of the joint distribution of X'AX/o” and X'BX

/o” is given by M(t1, t2) = |I – 2t1A – 212 B|T**, It, 3 ht, i = 1, 2, we have M(t1, t2) =

MOti, 0)M(0, t2), and the proof of the following

Since the moment-generating function of the joint distribution of X'AX/o” and X'BX

/o” is given by M(t1, t2) = |I – 2t1A – 212 B|T**, It, 3 ht, i = 1, 2, we have M(t1, t2) =

MOti, 0)M(0, t2), and the proof of the following

**theorem**is complete.**Theorem**2.### What people are saying - Write a review

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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