ISYE 2027 Chapter Notes - Chapter 13: Probability Mass Function, Standard Deviation, Random Variable
11 Apr 2017
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We shall denote the distribution function of each random variable xi by f, its expectation by ,and the standard deviation by . Average of first n random variables is. < = 1 , setting a= in chebyshev"s inequality. D: the a few rule. Most of the probability mass of a random variable is within a few standard deviations from its expectation: 13. 3: the law of the large numbers, the law of large numbers. If xn bar is the average of n independent random variables with expectation and variance 2 , then for any > 0: lim. "n: as n is larger, the probability for the average to be within a certain distance of the expectation increases, in the limit even to 1. If the averages do not converge, doing a longer simulation or more experiments would not make the distribution converge about the mean: strong law of large numbers: lim.
