## Introduction to mathematical statistics |

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Page 55

Since /^aa) is found by summing (or integrating) the joint p.d.f. f{x1, x2) over all x2

for a fixed x1, we can think of recording this sum in the "margin" of the a^avplane.

Accordingly, f^Xj) is called the

Since /^aa) is found by summing (or integrating) the joint p.d.f. f{x1, x2) over all x2

for a fixed x1, we can think of recording this sum in the "margin" of the a^avplane.

Accordingly, f^Xj) is called the

**marginal p.d.f.**of Xj. In Uke manner P 00 fz(x2) ...Page 59

Let the random variables X1, X2, . . ., Xn have the joint p.d.f. f(x1, x2, . . . , xn). If

the random variables are of the ... Up to this point, each

a p.d.f. of one random variable. It is convenient to extend this terminology to joint

...

Let the random variables X1, X2, . . ., Xn have the joint p.d.f. f(x1, x2, . . . , xn). If

the random variables are of the ... Up to this point, each

**marginal p.d.f.**has beena p.d.f. of one random variable. It is convenient to extend this terminology to joint

...

Page 114

From this joint p.d.f. g(y1, y2) we may obtain the

on y2 or the

emphasized that the technique of change of variables involves the introduction of

as ...

From this joint p.d.f. g(y1, y2) we may obtain the

**marginal p.d.f.**of Y1 by summingon y2 or the

**marginal p.d.f.**of Y2 by summing on yv Perhaps it should beemphasized that the technique of change of variables involves the introduction of

as ...

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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