## Introduction to Mathematical Statistics |

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Page 104

That is, the conditional p.d.f. of Y, given X = a, is itself normal with

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

the conditional

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) ...Page 148

The

Pty = X ki. and The following corollary of this theorem is quite useful. Corollary.

Let X1, ..., Xn denote the items of a random sample of size n from a distribution

that ...

The

**mean**and the variance of the linear function Y = S \,x, 1 are respectively nPty = X ki. and The following corollary of this theorem is quite useful. Corollary.

Let X1, ..., Xn denote the items of a random sample of size n from a distribution

that ...

Page 149

Determine the

from a distribution having p.d. f. f(x) = 4x", 0 < x < 1, zero elsewhere. > - 4.71. Let

X and Y be random variables with pi = 1, u2 = 4, of = 4, o: = 6, p = 4. Find the

Determine the

**mean**and variance of the**mean**X of a random sample of size 9from a distribution having p.d. f. f(x) = 4x", 0 < x < 1, zero elsewhere. > - 4.71. Let

X and Y be random variables with pi = 1, u2 = 4, of = 4, o: = 6, p = 4. Find the

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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