## 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

continuous type of random variable. We speak of a distribution function F(x) as

being of the continuous or

variable is of the ...

for the

**discrete type**of random variable, and F{x) = f(w)dw, •'-00 for thecontinuous type of random variable. We speak of a distribution function F(x) as

being of the continuous or

**discrete type**, depending on whether the randomvariable is of the ...

Page 48

If the p.d.f. of one or more variables of the continuous type or of the

is a constant on the space s/, we say that the probability is distributed uniformly

over j^Thns, in the example above, we say that X has a unj£orm_ distribution ...

If the p.d.f. of one or more variables of the continuous type or of the

**discrete type**is a constant on the space s/, we say that the probability is distributed uniformly

over j^Thns, in the example above, we say that X has a unj£orm_ distribution ...

Page 83

With x, held fast, and with /, (x, ) > 0, this function of x2 satisfies the conditions of

being a p.d.f. of a

nonnegative and We now define the symbol ^,i(x2|xi) by the relation f2\i(x2\xix) =^

, ...

With x, held fast, and with /, (x, ) > 0, this function of x2 satisfies the conditions of

being a p.d.f. of a

**discrete type**of random variable X2 because y(x,, x2)//i(x,) isnonnegative and We now define the symbol ^,i(x2|xi) by the relation f2\i(x2\xix) =^

, ...

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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