Independence of random variables and some applications
This chapter consists of two sections. In the first section, we introduce the concept of independence of r.v.'s and establish criteria for proving or disproving independence. Also, its relationship to uncorrelatedness is discussed. In the second section, the sample mean and the sample variance are defined, and some of their moments are also produced. The main thrust of this section, however, is the discussion of the reproductive property of certain distributions. As a by-product, we also obtain the distribution of the sample mean and of a certain multiple of the sample variance for independent and Normally distributed r.v.'s.
5.1 Independence of Random Variables and Criteria ...
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