## Introduction to Mathematical Statistics |

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Page 58

It is convenient to refer to these as the “

variance” of X2, given X1 = 21. Of course we have E{[X2 – E(X2|aci)]*|aci) = E(X}|

z1) — [E(X2|21)]” from an earlier result. In like manner, the

expectation ...

It is convenient to refer to these as the “

**conditional**mean” and the “**conditional**variance” of X2, given X1 = 21. Of course we have E{[X2 – E(X2|aci)]*|aci) = E(X}|

z1) — [E(X2|21)]” from an earlier result. In like manner, the

**conditional**expectation ...

Page 60

We shall next extend the definition of a

, ..., xn|a'i) is defined by the relation f(x1, 22, . . . , *..), f(x2, ..., walr1) = fi (r.1) and f(

x2, ..., zn|z1) is called the joint

We shall next extend the definition of a

**conditional**p.d.f. If f(z) > 0, the symbol f(x2, ..., xn|a'i) is defined by the relation f(x1, 22, . . . , *..), f(x2, ..., walr1) = fi (r.1) and f(

x2, ..., zn|z1) is called the joint

**conditional**p.d.f. of X2,..., Xn, given X1 = 21.Page 104

That is, the

02/01)(a – pu) and variance o:(1 — po). Thus, with a bivariate normal distribution,

the

That is, the

**conditional**p.d.f. of Y, given X = a, is itself normal with mean puz + p(02/01)(a – pu) and variance o:(1 — po). Thus, with a bivariate normal distribution,

the

**conditional**mean of Y, given X = a, is linear in a and is given by O. E(Y|z) ...### 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