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 65
If the variance of the random variable X exists, show that E(X2)>[E(X)]2. 1.93. Let
a random variable X of the continuous type have a p.d.f. f(x) whose graph is
symmetric with respect to x = c. If the mean value of X exists, show that E(X) = c.
If the variance of the random variable X exists, show that E(X2)>[E(X)]2. 1.93. Let
a random variable X of the continuous type have a p.d.f. f(x) whose graph is
symmetric with respect to x = c. If the mean value of X exists, show that E(X) = c.
Page 114
A fair die is cast at random three independent times. Let the random variable X,
be equal to the number of spots that appear on the /'th trial, 1,2,3. Let the random
variable Y be equal to max (A',). Find the distribution function and the p.d.f. of Y.
A fair die is cast at random three independent times. Let the random variable X,
be equal to the number of spots that appear on the /'th trial, 1,2,3. Let the random
variable Y be equal to max (A',). Find the distribution function and the p.d.f. of Y.
Page 156
let the random variables Xh i = 1, 2, . . . , n, be independent, each having the
same p.d.f. Ax) = px(l — p)x ~ \ x = 0, 1, and zero else- „ where. If Y =Y,Xh then Y
is b(n,p). It should be observed that i Y = u(Xx) = {Xx — n)\a is a function of A', that
...
let the random variables Xh i = 1, 2, . . . , n, be independent, each having the
same p.d.f. Ax) = px(l — p)x ~ \ x = 0, 1, and zero else- „ where. If Y =Y,Xh then Y
is b(n,p). It should be observed that i Y = u(Xx) = {Xx — n)\a is a function of A', that
...
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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 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 |