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 12
The Probability Set Function Let # denote the set of every possible outcome of a
random experiment; that is, # is the sample space. It is our purpose to define a set
function P{C) such that if C is a subset of #, then P{C) is the probability that the ...
The Probability Set Function Let # denote the set of every possible outcome of a
random experiment; that is, # is the sample space. It is our purpose to define a set
function P{C) such that if C is a subset of #, then P{C) is the probability that the ...
Page 18
Whether this probability set function is realistic can only be checked by
performing the random experiment a large number of times. EXERCISES 1.17. A
positive integer from one to six is to be chosen by casting a die. Thus the
elements c of the ...
Whether this probability set function is realistic can only be checked by
performing the random experiment a large number of times. EXERCISES 1.17. A
positive integer from one to six is to be chosen by casting a die. Thus the
elements c of the ...
Page 21
But these are precisely the conditions that a probability set function must satisfy.
Accordingly, P(C2\C\) is a probability set function, defined for subsets of Cx . It
may be called the conditional probability set function, relative to the hypothesis C,
; ...
But these are precisely the conditions that a probability set function must satisfy.
Accordingly, P(C2\C\) is a probability set function, defined for subsets of Cx . It
may be called the conditional probability set function, relative to the hypothesis C,
; ...
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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 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 Yx 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 statistic for 9 subset testing H0 theorem u(Xu X2 unbiased estimator XuX2 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 | 27 Jan 2010 |
| ISBN | 0023557222, 9780023557224 |
| Length | 564 pages |
| Export Citation | BiBTeX EndNote RefMan |