Speaker
Description
The classical coin tossing experiment is studied. Asymptotic theorems are obtained concerning the head-runs containing certain numbers of tails. It is proven that the limit distribution of the number of those runs of length 𝑛 containing at most 𝑇 tails is compound Poisson. The normalized first hitting time for the at most 𝑇 contaminated head runs is shown to have an exponential limiting distribution just like any other waiting time distribution. However, accompanying distributions are obtained for the length of the longest head-runs containing at most 𝑇 tails given that it does not have a limiting distribution. To this end, a two parameter family of accompanying distribution is offered. Simulation results supporting the theorems are also presented.
