Finding expected values of distributions is one of the main tasks of any probabilistic analysis. The expected value in the narrower sense of the average (mean), which is a measure of distribution location, is introduced first, followed by the related concepts of the median and distribution quantiles. Expected values of functions of random variables are presented, as well as the variance as the primary measure of the distribution scale. The discussion is extended to moments of distributions (skewness, kurtosis), as well as to two- and d-dimensional generalizations. Finally, propagation of errors is analyzed.
- 2.E. Brynjolfsson, Y.J. Hu, M.D. Smith, The longer tail: the changing shape of Amazon’s sales distribution curve. http://dx.doi.org/10.2139/ssrn.1679991. 20 Sep 2010
- 3.C. Anderson, The Long Tail: Why the Future of Business is Selling Less of More (Hyperion, New York, 2006)Google Scholar
- 4.F. James, Statistical Methods in Experimental Physics, 2nd edn. (World Scientific, Singapore, 2010)Google Scholar
- 5.Y. Viniotis, Probability and Random Processes for Electrical Engineers (WCB McGraw-Hill, Singapore, 1998)Google Scholar