CS 271 Randomness & Computation Fall 2011
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چکیده
So far we have talked about the expectation of random variables, and moved on to the variance or the second moment. However, neither of these methods is strong enough to produce the tight bounds needed for some applications. We have already stated that if all you are given is the variance of a r.v., then Chebyshev’s Inequality is essentially the best you can do. Thus, more information is needed to acheive substantially tighter bounds. We begin with the case in which the r.v. is the sum of a sequence of independent r.v.’s; this case arises very frequently in applications.
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