## 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 45

for the discrete type of random variable, and F(x) = f{w) dw, for the

continuous or discrete type, depending on whether the random variable is of the

...

for the discrete type of random variable, and F(x) = f{w) dw, for the

**continuous****type**of random variable. We speak of a distribution function F(x) as being of thecontinuous or discrete type, depending on whether the random variable is of the

...

Page 84

That is,^|i(x2|jc|) has the properties of a p.d.f. of one

variable. It is called the conditional p.d.f. of the

variable X2, given that the

xx .

That is,^|i(x2|jc|) has the properties of a p.d.f. of one

**continuous type**of randomvariable. It is called the conditional p.d.f. of the

**continuous type**of randomvariable X2, given that the

**continuous type**of random variable Xx has the valuexx .

Page 540

functions of the

, (X„, Y„) be a random sample from the joint distribution. Under H0, the order

statistics of Xu X2, . . . , X„ and the order statistics of Y\ , Y2, . . . , Y„ are,

respectively, ...

functions of the

**continuous type**, against all alternatives. Let (X\, Yx), (X2, Y2), . . ., (X„, Y„) be a random sample from the joint distribution. Under H0, the order

statistics of Xu X2, . . . , X„ and the order statistics of Y\ , Y2, . . . , Y„ are,

respectively, ...

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### Common terms and phrases

Accordingly approximate best critical region bivariate normal distribution 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 gamma distribution given H0 is true hypothesis H0 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 Xu 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 testing H0 theorem u(Xu X2 unbiased estimator variance a2 XuX2 Xx and X2 Yu Y2 zero elsewhere