Probability distribution of distances between local maximum of random number series

It is considered a sequence of random independent numbers. If x(1), x(2)., x(n) and so it is local maximum. Here it is showed that the probability mass function (PMF) f(m)(d) of distances d between local maxima is non-parametric. And the same will be for any probability distribution of random numbers in the sequence, and that the average distance is exactly 3. It is presented a method of computation of this PMF and its level for distances between 2 and 29. This PMF is confirmed to match distance distributions of sample random number sequences, which were created by pseudo generators of random number or obtained from "real" random number sources.