## Introduction to Mathematical Statistics |

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Page 87

A random variable X which has a p.d.f. of the form of f(z) is said to have a

indicates that the Poisson p.d. f. may be used in a number of applications with ...

A random variable X which has a p.d.f. of the form of f(z) is said to have a

**Poisson****distribution**, and any such f(z) is called a Poisson p.d. f. Remarks. Experienceindicates that the Poisson p.d. f. may be used in a number of applications with ...

Page 89

m + m” — m” = m. That is, a

account, a Poisson p.d. f. is frequently written preac! 3. a = 0, 1,2,..., f(x) = = 0

elsewhere. Thus the parameterm in a Poisson p.d.f. is the mean u. Table I in the

Appendix ...

m + m” — m” = m. That is, a

**Poisson distribution**has p = q^ = m > 0. On thisaccount, a Poisson p.d. f. is frequently written preac! 3. a = 0, 1,2,..., f(x) = = 0

elsewhere. Thus the parameterm in a Poisson p.d.f. is the mean u. Table I in the

Appendix ...

Page 90

probability that there are exactly five blemishes in 3000 feet of wire is 35e-3 and,

by Table I of the Appendix, Pr(X = 5) = Pr(X s 5) — Pr(X = 4) = 0.101,

approximately.

**Poisson distribution**with mean 3000(rood) = 3. Thus, for illustration, theprobability that there are exactly five blemishes in 3000 feet of wire is 35e-3 and,

by Table I of the Appendix, Pr(X = 5) = Pr(X s 5) — Pr(X = 4) = 0.101,

approximately.

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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