## Introduction to mathematical statistics |

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Page 47

The preceding theorem is a generalization of an

Chebyshev's

Chebyshev's

probability ...

The preceding theorem is a generalization of an

**inequality**which is often calledChebyshev's

**inequality**. This**inequality**will now be established. Theorem 7.~Chebyshev's

**Inequality**. Let the random variable X have a distribution ofprobability ...

Page 48

Then we have Since the numerator of the right-hand member of the preceding

result. Naturally, we would take the positive number k to be greater than one to ...

Then we have Since the numerator of the right-hand member of the preceding

**inequality**is a2, the**inequality**may be written Pr(|Z-H >H <1, which is the desiredresult. Naturally, we would take the positive number k to be greater than one to ...

Page 238

Then the variance of Z satisfies

sufficient statistic for 9. We make the unnecessary assumption of the existence of

a sufficient statistic in order to give a relatively short proof of the

Then the variance of Z satisfies

**Inequality**(1) without regard to the existence of asufficient statistic for 9. We make the unnecessary assumption of the existence of

a sufficient statistic in order to give a relatively short proof of the

**inequality**.### What people are saying - Write a review

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere