A note on the coincidence of some random functions

This paper deals with a system capable of randomly attaining two states “on” and “off". For convenience this system is pictured as a pulse train. The question is, what is the expected amount of time that $n$ of such systems are in the same state simultaneously. The answer is shown to depend on the probability of a system being in a given state at a specified time. A formal solution for the Laplace transform of this probability is given.