## Introduction to mathematical statistics |

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Page 11

1.4 The

of a random experiment; that is, s/ is the sample space. It is our purpose to define

a set function P(A) such that if A is a subset of si ', then P(A) is the probability that

...

1.4 The

**Probability Set Function**Let j# denote the set of every possible outcomeof a random experiment; that is, s/ is the sample space. It is our purpose to define

a set function P(A) such that if A is a subset of si ', then P(A) is the probability that

...

Page 26

Here also, the theorem is intuitively appealing because, as h tends to zero, the

limit of the set {x; a < x < a + h) is the null set. ... The definition of the distribution

function makes it clear that the

distribution ...

Here also, the theorem is intuitively appealing because, as h tends to zero, the

limit of the set {x; a < x < a + h) is the null set. ... The definition of the distribution

function makes it clear that the

**probability set function**P determines thedistribution ...

Page 51

But these are precisely the conditions that a

Accordingly, P(A2\A1) is a

may be called the conditional

A1; ...

But these are precisely the conditions that a

**probability set function**must satisfy.Accordingly, P(A2\A1) is a

**probability set function**, defined for subsets of A1. Itmay be called the conditional

**probability set function**, relative to the hypothesisA1; ...

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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