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 75
We now formulate the definition of the space of two random variables. Definition
1. Given a random experiment with a sample space c€. Consider two random
variables Xx and X2, which assign to each element c of ^ one and only one
ordered ...
We now formulate the definition of the space of two random variables. Definition
1. Given a random experiment with a sample space c€. Consider two random
variables Xx and X2, which assign to each element c of ^ one and only one
ordered ...
Page 101
upon xx . Then the marginal p.d.f. of X2 is, for random variables of the continuous
type, flix2)= /2|l(x2lxl)/l(xl)<&l •'-00 = fi\\(,x2\xx) fx(xx)dxx •'-00 =y2|l(-x:2l^:i)-
Accordingly, f22{x2) =f2\x(.x2\x\) and ./(x„ x2) =Mxi)f2(x2), when /2|l (^2^1 ) does
not ...
upon xx . Then the marginal p.d.f. of X2 is, for random variables of the continuous
type, flix2)= /2|l(x2lxl)/l(xl)<&l •'-00 = fi\\(,x2\xx) fx(xx)dxx •'-00 =y2|l(-x:2l^:i)-
Accordingly, f22{x2) =f2\x(.x2\x\) and ./(x„ x2) =Mxi)f2(x2), when /2|l (^2^1 ) does
not ...
Page 107
With random variables of the discrete type, the proof is made by using summation
instead of integration. EXERCISES 2.28. Show that the random variables Xx and
X2 with joint p.d.f. /(x,, x2) = 12x,x2(1 — x2), 0 < jc] < 1, 0 < x2 < 1, zero ...
With random variables of the discrete type, the proof is made by using summation
instead of integration. EXERCISES 2.28. Show that the random variables Xx and
X2 with joint p.d.f. /(x,, x2) = 12x,x2(1 — x2), 0 < jc] < 1, 0 < x2 < 1, zero ...
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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 |