## 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 88

We call E[

) of

case. We also note that the expected value of X2 can be found in two ways: E(X2)

...

We call E[

**u**(**Xu X2**)] the expectation (mathematical expectation or expected value) of

**u**(**Xu X2**), and it can be shown to be a linear operator as in the one-variablecase. We also note that the expected value of X2 can be found in two ways: E(X2)

...

Page 109

Incidentally, except for a set of probability measure zero, we have d'F(x,y,z) =f(x, y

, z). dx dy dz Let XuX2, . . . ,X„ be random variables having joint p.d.f. f(xu x2, . . . ,

x„) and let

Incidentally, except for a set of probability measure zero, we have d'F(x,y,z) =f(x, y

, z). dx dy dz Let XuX2, . . . ,X„ be random variables having joint p.d.f. f(xu x2, . . . ,

x„) and let

**u**(**Xu X2**, . . . , X„) be a function of these variables such that the «-fold ...Page 262

Consider a random sample

OeQ. ... Suppose that we can find a nontrivial function of

Consider a random sample

**Xu X2**, . . . , X„ from a distribution having p.d.f. f(x; 9),OeQ. ... Suppose that we can find a nontrivial function of

**xu x2**, . . . , x„, say**u**(x\ ,**x2**, . . . , x„), such that, when 6 is replaced by**u**(x\ ,**x2**, . . . , x„), the likelihood ...### What people are saying - Write a review

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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