## Introduction to Mathematical Statistics |

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Page 27

We wish primarily to establish their names and some of their properties. 2.1. Two

Discrete-Type Distributions. In this section we introduce the binomial and

Poisson distributions. (a) The

integer, ...

We wish primarily to establish their names and some of their properties. 2.1. Two

Discrete-Type Distributions. In this section we introduce the binomial and

Poisson distributions. (a) The

**binomial distribution**. Recall that if n is a positiveinteger, ...

Page 144

Since there exists a distribution, namely, the Poisson distribution with mean u,

that has this moment-generating ... The result of this example enables us to use

the Poisson distribution as an approximation to the

is ...

Since there exists a distribution, namely, the Poisson distribution with mean u,

that has this moment-generating ... The result of this example enables us to use

the Poisson distribution as an approximation to the

**binomial distribution**when nis ...

Page 149

+ Xn, it is known, page 50, that Y has a

and p. Calculation of probabilities concerning Y, when we do not use the Poisson

approximation, can be greatly simplified by making use of the fact that (Y ...

+ Xn, it is known, page 50, that Y has a

**binomial distribution**with parameters nand p. Calculation of probabilities concerning Y, when we do not use the Poisson

approximation, can be greatly simplified by making use of the fact that (Y ...

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Accordingly best critical region binomial distribution cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere