## 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 In X. What is the p.d.f. of Y? 3.4 The

Normal Distribution Consider the

exists because the integrand is a positive continuous function which is bounded

by ...

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

Normal Distribution Consider the

**integral**I = P exp(-y2/2)<fy. J — 00 This**integral**exists because the integrand is a positive continuous function which is bounded

by ...

Page 344

We shall evaluate the

shall subsequently set t1 = t2 — . . . = tn = 0, and thus establish Equation (1). First

we change the variables of integration in

...

We shall evaluate the

**integral**(2) c I V . . f. exp [i'x - (x = ^ = "] ^ . . . and then weshall subsequently set t1 = t2 — . . . = tn = 0, and thus establish Equation (1). First

we change the variables of integration in

**integral**(2) from x1, x2, . . . , xn to y1, y2,...

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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