## Introduction to mathematical statistics |

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Page 179

are mutually stochastically independent and each, in accordance with Theorem 1

, has a uniform distribution on the interval (0, 1). Thus F(X1), F(X2), .... F(Xn) is a ...

**Consider**the random variables F(X1), F(X2), . . . , F(Xn). These random variablesare mutually stochastically independent and each, in accordance with Theorem 1

, has a uniform distribution on the interval (0, 1). Thus F(X1), F(X2), .... F(Xn) is a ...

Page 272

0 is rejected, and the alternative composite hypothesis H1 : 0 > 0 is accepted if

and only if the observed mean x of a random sample of size 25 is greater than or

...

**Consider**a normal distribution of the form n(8, 4). The simple hypothesis H0: 8 =0 is rejected, and the alternative composite hypothesis H1 : 0 > 0 is accepted if

and only if the observed mean x of a random sample of size 25 is greater than or

...

Page 310

Let a and b denote positive integers greater than one and let n = ab.

random sample of size n = ab from this normal distribution. The items of the

random sample will be denoted by the symbols: -^11. -^12. ..., -^l/i ..., X1b -^21, -^

22, ...

Let a and b denote positive integers greater than one and let n = ab.

**Consider**arandom sample of size n = ab from this normal distribution. The items of the

random sample will be denoted by the symbols: -^11. -^12. ..., -^l/i ..., X1b -^21, -^

22, ...

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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