## Introduction to mathematical statistics |

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Page 188

-oo < y < e, = 1, 9 < y < co, is a distribution function. Moreover, lim Fn(y) = F(^) at

each point of continuity of In accordance with the definition of a

function F(y).

-oo < y < e, = 1, 9 < y < co, is a distribution function. Moreover, lim Fn(y) = F(^) at

each point of continuity of In accordance with the definition of a

**limiting****distribution**, the random variable Y has a**limiting distribution**with distributionfunction F(y).

Page 190

is a distribution function which is everywhere continuous and lim Gn(z) = n-»Co G

(z) at all points. Thus Z has a

This affords us an example of a

is a distribution function which is everywhere continuous and lim Gn(z) = n-»Co G

(z) at all points. Thus Z has a

**limiting distribution**with distribution function G(z).This affords us an example of a

**limiting distribution**that is not degenerate.Page 194

Let Y have a distribution which is b(n, p). Suppose that the mean p = np is the

same for every n; that is, p = p/n, where /x is a constant. We shall find the

Let Y have a distribution which is b(n, p). Suppose that the mean p = np is the

same for every n; that is, p = p/n, where /x is a constant. We shall find the

**limiting****distribution**of the binomial distribution, when p = p/n, by finding the limit of M(t; n).### What people are saying - Write a review

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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