From binomial distribution of electron occurrence to Gauss and Gauss-exponential distribution of the statistical time delay: Analytical transition and simulations

Starting from the binomial distribution for the electron occurrence in the interelectrode space, the Gaussian and mixed Gauss-exponential distribution for the statistical time delay are theoretically derived based on physical grounds. The analytical transition from discrete (number) representation to continuous (time) representation is accompanied by the Monte Carlo simulation of the statistical time delay distributions