## Introduction to Mathematical Statistics |

### From inside the book

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Page 37

Example 4. Let us divide, at random, a horizontal line segment of length five into

two parts. If X is the length of the left-hand part, it is reasonable to assume that X

has the p.d.f. f(r) #, 0 < a. ~ 5, 0 elsewhere. The

...

Example 4. Let us divide, at random, a horizontal line segment of length five into

two parts. If X is the length of the left-hand part, it is reasonable to assume that X

has the p.d.f. f(r) #, 0 < a. ~ 5, 0 elsewhere. The

**expected**value of the length X is...

Page 72

Theorem 3. Let the stochastically independent random variables X, and X2 have

the marginal probability density functions f(x1) and fa(x2) respectively. The

of X2 ...

Theorem 3. Let the stochastically independent random variables X, and X2 have

the marginal probability density functions f(x1) and fa(x2) respectively. The

**expected**value of the product of a function u(XI) of X1 alone and a function v(X2)of X2 ...

Page 153

The length of the random interval is Y(1/3.25 – 1/20.5) = 0.26Y, approximately.

Since E(Y/o”) = 10, we have E(Y) = 100°. Accordingly, the

length of the random interval is 2.60°. EXERCISES ` 5.1. Let the random variable

X ...

The length of the random interval is Y(1/3.25 – 1/20.5) = 0.26Y, approximately.

Since E(Y/o”) = 10, we have E(Y) = 100°. Accordingly, the

**expected**value of thelength of the random interval is 2.60°. EXERCISES ` 5.1. Let the random variable

X ...

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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