## Introduction to mathematical statistics |

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Page 79

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

will be denoted by the symbol b(n, p). The constants n and p are called the ...

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

**binomial****distribution**, and any such f(x) is called a binomial p.d.f. A**binomial distribution**will be denoted by the symbol b(n, p). The constants n and p are called the ...

Page 194

Let Y have a distribution which is b(n, p). Suppose that the mean p = np is the

same for every n; that is, p = p/n, where /x is a constant. We shall find the limiting

distribution of the

Let Y have a distribution which is b(n, p). Suppose that the mean p = np is the

same for every n; that is, p = p/n, where /x is a constant. We shall find the limiting

distribution of the

**binomial distribution**, when p = p/n, by finding the limit of M(t; n).Page 379

Index Analysis of variance, 320, 326 Approximate

300 normal for

of X, 196, 198 Poisson for

164 ...

Index Analysis of variance, 320, 326 Approximate

**distribution**(s), chi- square,300 normal for

**binomial**, 199 normal for chi-square, 194 normal for Poisson, 195of X, 196, 198 Poisson for

**binomial**, 194 Bayes' formula, 54 Bayesian statistics,164 ...

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### Common terms and phrases

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