## Introduction to Mathematical Statistics |

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Page 36

The n-fold

mathematical expectation, denoted by E[u(X1, X2,..., Xn)], of the function u(X1,X2,

..., Xn). In this paragraph we shall point out some fairly obvious but useful facts

about ...

The n-fold

**integral**(or the n-fold sum, as the case may be) is called themathematical expectation, denoted by E[u(X1, X2,..., Xn)], of the function u(X1,X2,

..., Xn). In this paragraph we shall point out some fairly obvious but useful facts

about ...

Page 96

Find the distribution function of Y = —2 ln X. What is the p.d.f. of Y2 3.4 The

Normal Distribution Consider the

because the integrand is a positive continuous function which is bounded by an ...

Find the distribution function of Y = —2 ln X. What is the p.d.f. of Y2 3.4 The

Normal Distribution Consider the

**integral**I = J. exp(-y”/2) dy. This**integral**existsbecause the integrand is a positive continuous function which is bounded by an ...

Page 344

We shall evaluate the

we shall subsequently set ti = t2 = . . . = t = 0, and thus establish Equation (1). First

we change the variables of integration in

...

We shall evaluate the

**integral**(2) cs - - - s exp |ex - e-oo-e da, - - - dra, and thenwe shall subsequently set ti = t2 = . . . = t = 0, and thus establish Equation (1). First

we change the variables of integration in

**integral**(2) from 21, a2, ..., a.m to yi, y2,...

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### Common terms and phrases

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