## Introduction to Mathematical Statistics |

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Page 20

Similarly, after extending the definition of a p.d.f. of the discrete type, we replace,

for one random variable, 2/0) by X f(x), ... If f(z) is the p.d.f. of a

random variable X and if A is the set {x; a 3 x < b), then P(A) = Pr(X e A) can be ...

Similarly, after extending the definition of a p.d.f. of the discrete type, we replace,

for one random variable, 2/0) by X f(x), ... If f(z) is the p.d.f. of a

**continuous type**ofrandom variable X and if A is the set {x; a 3 x < b), then P(A) = Pr(X e A) can be ...

Page 23

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

...

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 57

It is evident that f(z2|aci) is nonnegative and that co * f(x1, x2) J. solo da:2 = - oc

Tsū) data - so J. f(x1, x2) da'a 1 fi(x1) That is, f(z2|aci) has the properties of a p.d.f.

of one

...

It is evident that f(z2|aci) is nonnegative and that co * f(x1, x2) J. solo da:2 = - oc

Tsū) data - so J. f(x1, x2) da'a 1 fi(x1) That is, f(z2|aci) has the properties of a p.d.f.

of one

**continuous type**of random variable. It is called the conditional p.d.f. of 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