## Introduction to mathematical statistics |

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In Example 4 of this section, we selected c1 = -V 0.05 and c2 = 1 in order to

obtain a 95 per cent confidence interval for 8. However, there are many ways of ...

From this result

**show**how to construct a 95 per cent confidence interval for 9. 6.4.In Example 4 of this section, we selected c1 = -V 0.05 and c2 = 1 in order to

obtain a 95 per cent confidence interval for 8. However, there are many ways of ...

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an(i the variance of <p(Yi). 8.15. Let the random variables X and Y have the joint

p.d.f. f(x, y) = (2/02)e~(x + 1/)/fl, 0 < x < y < 00, zero elsewhere. (a)

**Show**that Y2 is an unbiased statistic for 9 with variance 82. Find £(^2^1) = 9(1/1)an(i the variance of <p(Yi). 8.15. Let the random variables X and Y have the joint

p.d.f. f(x, y) = (2/02)e~(x + 1/)/fl, 0 < x < y < 00, zero elsewhere. (a)

**Show**that the ...Page 352

generating function of Q/a2. 13.7. Let A be a real symmetric matrix. Prove that

each of the nonzero characteristic numbers of A is equal to one if and only if A2 =

A. Hint.

**Show**that Q/aa does not have a chi-square distribution. Find the moment-generating function of Q/a2. 13.7. Let A be a real symmetric matrix. Prove that

each of the nonzero characteristic numbers of A is equal to one if and only if A2 =

A. Hint.

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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