ABSTRACT
In this chapter we review a few important results from the theory of probability.
Let X1, ..., XN be N independent real random variables with the same mean (that is, expected value) μ and same variance σ2. The main consequence of independence is that E(XiXj) = E(Xi)E(Xj) = μ
2 for i = j. Then, it is easily shown that the sample average
X¯ = N−1 N∑
Xn
has μ for its mean and σ2/N for its variance.
