## 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(x) as being of the continuous or

...

We speak of a distribution function F(x) 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. /(x) has at...

Page 56

We shall now discuss the notion of a conditional p.d.f. Let X1 and X2 denote

random variables of the

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

marginal ...

We shall now discuss the notion of a conditional p.d.f. Let X1 and X2 denote

random variables of the

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

marginal ...

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### Common terms and phrases

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