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In this chapter, we introduce somewhat informally and intuitively the notion of mathematical expectation as a probability-weighted average. We present various mathematical forms and a useful interpretation of the concept, then obtain the mean values (expectations) for a number of standard distributions. In the process, we exhibit the integral character of mathematical expectation. In the next chapter, we elucidate that integral character by examining the relationship between mathematical expectation and the Lebesgue integral. The extensive literature on the Lebesgue integral provides important resources, for both applications and the further development of the probability model. For the current development, we operate quite informally.
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