## 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 201

Let Y, < Y2 < Y3 < Y4 be the

distribution having p.d.f. /(x) = e~x, 0 < x < oo, zero elsewhere. Find Pr (3 < r4).

4.57. Let Xx , X2, X3 be a random sample from a distribution of the continuous ...

Let Y, < Y2 < Y3 < Y4 be the

**order statistics**of a random sample of size 4 from thedistribution having p.d.f. /(x) = e~x, 0 < x < oo, zero elsewhere. Find Pr (3 < r4).

4.57. Let Xx , X2, X3 be a random sample from a distribution of the continuous ...

Page 499

Let the following numbers represent the values of the

observations obtained in a random sample from a certain distribution of the

continuous type: 61, 69, 71, 74, 79, 80, 83, 84, 86, 87, 92, 93, 96, 100, 104, 105,

113, ...

Let the following numbers represent the values of the

**order statistics**of n = 27observations obtained in a random sample from a certain distribution of the

continuous type: 61, 69, 71, 74, 79, 80, 83, 84, 86, 87, 92, 93, 96, 100, 104, 105,

113, ...

Page 500

Y9 are the

continuous type. 11.4. Find the smallest value of « for which Pr(y, < <J0j < Y„) >

0.99, where Yx < □ . □ < Y„ are the

...

Y9 are the

**order statistics**of a random sample of size 9 from a distribution of thecontinuous type. 11.4. Find the smallest value of « for which Pr(y, < <J0j < Y„) >

0.99, where Yx < □ . □ < Y„ are the

**order statistics**of a random sample of size n...

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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