## Introduction to mathematical statistics |

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Page 148

Let X1, . . . , Xn denote the items of a random sample of size nfrom a distribution

that has mean jj. and

are respectively fiY = (2 k^p and aY = i ' i dU>2- i n Example 3. Let X = 2 XJn

denote ...

Let X1, . . . , Xn denote the items of a random sample of size nfrom a distribution

that has mean jj. and

**variance a2**. The mean and n n the variance of Y = 2 ^t^iare respectively fiY = (2 k^p and aY = i ' i dU>2- i n Example 3. Let X = 2 XJn

denote ...

Page 149

Find the mean and variance of Z = 3X — 2Y. 4.72. Let X and Y be stochastically

independent random variables with means fi1, p2 and

Determine the correlation coefficient of X and Z = X — Y in terms of fi1, p2, a\, a|.

4.73.

Find the mean and variance of Z = 3X — 2Y. 4.72. Let X and Y be stochastically

independent random variables with means fi1, p2 and

**variances a2**, a$.Determine the correlation coefficient of X and Z = X — Y in terms of fi1, p2, a\, a|.

4.73.

Page 156

Let X have a normal distribution with unknown parameters Mi and

modification can be made in conducting the experiment so that the

the distribution will remain the same but the mean of the distribution will be

changed; say, ...

Let X have a normal distribution with unknown parameters Mi and

**a2**. Amodification can be made in conducting the experiment so that the

**variance**ofthe distribution will remain the same but the mean of the distribution will be

changed; say, ...

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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