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. |
From inside the book
Results 1-3 of 47
Page 126
3.2 The Poisson Distribution Recall that the series converges, for all values of m,
to em. Consider the function /(x) defined by mxe-m f(x) = , , x = 0,1,2,..., = 0
elsewhere, where m > 0. Since m > 0, then /(X) > 0 and x x = 0 A- x = 0 A- that is,/(
x) ...
3.2 The Poisson Distribution Recall that the series converges, for all values of m,
to em. Consider the function /(x) defined by mxe-m f(x) = , , x = 0,1,2,..., = 0
elsewhere, where m > 0. Since m > 0, then /(X) > 0 and x x = 0 A- x = 0 A- that is,/(
x) ...
Page 130
If the random variable X has a Poisson distribution such that Pr (X = 1) = Pr (X = 2
), find Pr (X = 4). 3.23. The m.g.f. of a random variable X is eMe' ~ l). Show that Pr
(jx - 2a < X < n + 2a) = 0.931. 3.24. In a lengthy manuscript, it is discovered that ...
If the random variable X has a Poisson distribution such that Pr (X = 1) = Pr (X = 2
), find Pr (X = 4). 3.23. The m.g.f. of a random variable X is eMe' ~ l). Show that Pr
(jx - 2a < X < n + 2a) = 0.931. 3.24. In a lengthy manuscript, it is discovered that ...
Page 244
We shall find the limiting distribution of the binomial distribution, when p = n/n, by
finding the limit of M(t; n). ... Since there exists a distribution, namely the Poisson
distribution with mean that has this m.g.f. e^e' ~ ", then, in accordance with the ...
We shall find the limiting distribution of the binomial distribution, when p = n/n, by
finding the limit of M(t; n). ... Since there exists a distribution, namely the Poisson
distribution with mean that has this m.g.f. e^e' ~ ", then, in accordance with the ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
Common terms and phrases
Accordingly approximate best critical region 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 F-distribution gamma distribution given H0 is true hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu percent confidence interval 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 sufficient statistic testing H0 theorem unbiased estimator variance a2 Xx and X2 Yu Y2 zero elsewhere
Bibliographic information
| Title | Introduction to Mathematical Statistics Prentice Hall International Editions |
| Author | Robert V. Hogg |
| Contributor | Allen Thornton Craig |
| Edition | 5, illustrated |
| Publisher | Prentice Hall, 1995 |
| Original from | the University of Michigan |
| Digitized | 3 Feb 2010 |
| ISBN | 0023557222, 9780023557224 |
| Length | 564 pages |
| Export Citation | BiBTeX EndNote RefMan |