6.042J Lecture Notes - Lecture 16: Cumulative Distribution Function, Lazy Susan, Pairwise Independence
13 Apr 2016
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It is safe to rearrange terms in sums because we implicitly assume that the de ning sum for the expectation is absolutely convergent. We cab estimate averages by estimating expectations of random variables based on picking from random elements. Total expectation of the number of heads given n ips: Informally, a random variable is a number produced by a random process. For example, the number of heads gotten when a fair coin is ipped. Formally, a random variable is a total function that maps outcomes of the sample space to numbers. Random variables are mutually independent iff the events that they de ne are mutually independent. The indicator for event a is 1 if a occurs and 0 if a does not occur. If r is dependent of s, then r is independent of any information about s. K-way independence: any k of the variables are mutually independent. Uniform random variables means all values are equally likely.
