## Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |

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Page 82

Let f(x, y) = e~x~y, 0 < jc < oo, 0 < >> < oo, zero elsewhere, be the p.d.f. of X and

Y. Then if Z = * + y, compute Pr (Z < 0), Pr (Z ... (a) Write these probabilities in a

rectangular array as in Example 2, recording each

Let f(x, y) = e~x~y, 0 < jc < oo, 0 < >> < oo, zero elsewhere, be the p.d.f. of X and

Y. Then if Z = * + y, compute Pr (Z < 0), Pr (Z ... (a) Write these probabilities in a

rectangular array as in Example 2, recording each

**marginal p.d.f.**in the "margins.Page 110

Now, however, let us take any group of k < n of these random variables and let us

find the joint p.d.f. of them. This joint p.d.f. is called the

particular group of k variables. To fix the ideas, take n = 6, k = 3, and let us select

the ...

Now, however, let us take any group of k < n of these random variables and let us

find the joint p.d.f. of them. This joint p.d.f. is called the

**marginal p.d.f.**of thisparticular group of k variables. To fix the ideas, take n = 6, k = 3, and let us select

the ...

Page 165

From this joint p.d.f. g(yuy2) 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(yuy2) we may obtain the

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

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

as ...

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Accordingly approximate best critical region bivariate normal distribution chi-square distribution complete sufficient statistic conditional p.d.f. conditional probability confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random depend upon 9 discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters equation estimator of 9 Example Exercise gamma distribution given H0 is true hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 likelihood function limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random sample random variables Xx reject H0 respectively sample space Section Show significance level simple hypothesis statistic for 9 testing H0 theorem u(Xu X2 unbiased estimator variance a2 XuX2 Xx and X2 Yu Y2 zero elsewhere