Christopher Murphy

The Law of Large Numbers is an important result from probability theorythat describes the outcome of repeating an experiment a large number oftimes. In this talk, we identify the set of all infinite sequences of cointosses, B, with the half open unit interval. From there we will look at howwe can use some basic facts in measure theory and the Borel principle tocalculate the probabilities of events inB. We will define the Rademacherfunctions and then prove a special case of Chebyshev’s inequalityinvolving nonnegative, piecewise constant functions. These tools are thenused to provide a proof for the Weak Law of Large Numbers for infinitesequences of coin tosses.