## 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

k2O2 Since the numerator of the right-hand member of the preceding

is o”, the

would take the positive number k to be greater than one to have an

k2O2 Since the numerator of the right-hand member of the preceding

**inequality**is o”, the

**inequality**may be written 1 which is the desired result. Naturally, wewould take the positive number k to be greater than one to have an

**inequality**of ...Page 278

the

, as 6Xr, 459m - 200 ln 9. —ln 9 < — This

c.(n) = + n – # in 9 < + n + + ln 9 = c(n). 153 100 Ş z - 153, a 100 2 * * > → 3 ...

the

**inequality**ko = 1 < L(75, n) ; : ### - 9 = } can be rewritten, by taking logarithms, as 6Xr, 459m - 200 ln 9. —ln 9 < — This

**inequality**is equivalent to the**inequality**c.(n) = + n – # in 9 < + n + + ln 9 = c(n). 153 100 Ş z - 153, a 100 2 * * > → 3 ...

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere