## 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 21

But these are precisely the conditions that a probability set function must satisfy.

Accordingly, P(C2|C,) is a probability set function, defined for subsets of C\ . It

may be called the

; ...

But these are precisely the conditions that a probability set function must satisfy.

Accordingly, P(C2|C,) is a probability set function, defined for subsets of C\ . It

may be called the

**conditional probability**set function, relative to the hypothesis C,; ...

Page 23

+ P(Ck)P(C\Ck) = £ P(QP(C|C,). i = i This result is sometimes called the law of

total probability. From the definition of

law of total probability, that r<r\r\ f(CnC>) PJCj)PjC\Cj) nL.j\L,)- - nC' £ />(C,)/>(C|C

,) ...

+ P(Ck)P(C\Ck) = £ P(QP(C|C,). i = i This result is sometimes called the law of

total probability. From the definition of

**conditional probability**, we have, using thelaw of total probability, that r<r\r\ f(CnC>) PJCj)PjC\Cj) nL.j\L,)- - nC' £ />(C,)/>(C|C

,) ...

Page 27

(b) Compute the probability that the first blue chip appears on the third draw. 1.35

. A hand of 13 cards is to be dealt at random and without replacement from an

ordinary deck of playing cards. Find the

(b) Compute the probability that the first blue chip appears on the third draw. 1.35

. A hand of 13 cards is to be dealt at random and without replacement from an

ordinary deck of playing cards. Find the

**conditional probability**that there are at ...### What people are saying - Write a review

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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