## Introduction to Mathematical Statistics |

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Page 16

The two types of distributions that we shall describe by a probability density

function are called, respectively, the

simplicity of presentation, we first consider a distribution of one random variable.

The two types of distributions that we shall describe by a probability density

function are called, respectively, the

**discrete type**and the continuous type. Forsimplicity of presentation, we first consider a distribution of one random variable.

Page 23

We speak of a distribution function F(z) as being of the continuous or

...

We speak of a distribution function F(z) as being of the continuous or

**discrete****type**depending on whether the random variable is of the continuous or**discrete****type**. Remark. If X is a random variable of the continuous type, the p.d.f. f(z) has at...

Page 56

We shall now discuss the notion of a conditional p.d. f. Let Xi and X2 denote

random variables of the

positive on 9/ and is zero elsewhere. Let fi(x1) and f2(x2) denote respectively the

...

We shall now discuss the notion of a conditional p.d. f. Let Xi and X2 denote

random variables of the

**discrete type**which have the joint p.d. f. f(x1, x2) that ispositive on 9/ and is zero elsewhere. Let fi(x1) and f2(x2) denote respectively 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