## Introduction to mathematical statistics |

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every set A, A u 4 =4.

u 42 u ...

**Example**4. Let A1 and A2 be defined as in**Example**1. Then A1 u A2 = A2.**Example**5. Let A2 = 0. Then 41 u .42 = A1 for every set ^41.**Example**6. Forevery set A, A u 4 =4.

**Example**7. Let 4fc = {x; l/(k + 1) ^ x < 1}, A = 1, 2, 3 Then .4ju 42 u ...

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respectively, by three intersecting circles. Then the sets (A1 u A2) n A3 and (A1 n

A2) u43 are depicted in Figure 1.2. Definition 5. In certain discussions or

considerations ...

**Example**13. Let A1, A2, and A3 represent the sets of points enclosed,respectively, by three intersecting circles. Then the sets (A1 u A2) n A3 and (A1 n

A2) u43 are depicted in Figure 1.2. Definition 5. In certain discussions or

considerations ...

Page 293

In

variables yield x = 0.6 and 2 (^i — x)2 = 3.6. If the test derived i in that

used, do we accept or reject H0: 8X = 0 at the 5 per cent significance level ? 11.2.

In

**Example**1, let n = 10, and let the experimental'values of the 10 _ randomvariables yield x = 0.6 and 2 (^i — x)2 = 3.6. If the test derived i in that

**example**isused, do we accept or reject H0: 8X = 0 at the 5 per cent significance level ? 11.2.

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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