## Introduction to mathematical statistics |

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Page 59

We have pr (o <

conditional probability density functions from the point of view of n

We have pr (o <

**X1**< >|*a = |) = j;,a/(,|) ^ = j;2 g) dX1 = \ but / i\ r1/2 r1/2 3 Pr (0 <**X1**< i) = J ^ = J 2(1 - xj ^ = i We shall now discuss the notions of marginal andconditional probability density functions from the point of view of n

**random****variables**.Page 68

and d*m 0) 8t1 8t2 yield the means, the variances, and the covariance of the two

means, variances, and correlation coefficients denoted by Mj, /x3; af, a\, a§; and

P12.

and d*m 0) 8t1 8t2 yield the means, the variances, and the covariance of the two

**random variables**. 2.24. Let**X1**, X2, and X3 be three**random variables**withmeans, variances, and correlation coefficients denoted by Mj, /x3; af, a\, a§; and

P12.

Page 74

With random variables of the discrete type, the proof is made by using summation

instead of integration. Let the

p.d.f. f(x1, x2, . . . , xn) and the marginal probability density functions fi[xi),fa(x2),...

With random variables of the discrete type, the proof is made by using summation

instead of integration. Let the

**random variables X1**, X2, . . . , Xn have the jointp.d.f. f(x1, x2, . . . , xn) and the marginal probability density functions fi[xi),fa(x2),...

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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