## Introduction to mathematical statistics |

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Page 60

A(*i) and f(x2, . . ., xn\xj] is called the joint conditional p.d.f. of X2, . . . , Xn,

X1 = x1. The joint conditional p.d.f. of any n — 1 random variables, say, X1, . . .,

Xt_1, Xl + 1, . . ., Xn,

A(*i) and f(x2, . . ., xn\xj] is called the joint conditional p.d.f. of X2, . . . , Xn,

**given**X1 = x1. The joint conditional p.d.f. of any n — 1 random variables, say, X1, . . .,

Xt_1, Xl + 1, . . ., Xn,

**given**Xt = xt, is defined as the joint p.d.f. of X1, X2, . . ., Xn ...Page 104

Y,

with mean /x2 + p(a2/ai)(x — Mi) and variance a|(l — p2). Thus, with a bivariate

normal distribution, the conditional mean of Y,

Y,

**given**that X = x. That is, the conditional p.d.f. of Y,**given**X = x, is itself normalwith mean /x2 + p(a2/ai)(x — Mi) and variance a|(l — p2). Thus, with a bivariate

normal distribution, the conditional mean of Y,

**given**X = x, is linear in x and is ...Page 251

If the loss function is

conditional distribution of 0,

the fact (Exercise 1.61) that £(|W — b\), if it exists, is a minimum when b is equal

to any ...

If the loss function is

**given**by £C[8, w(y)] = \8 — w(y)\, then a median of theconditional distribution of 0,

**given**Y = y, is the Bayes' solution. This follows fromthe fact (Exercise 1.61) that £(|W — b\), if it exists, is a minimum when b is equal

to any ...

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere