Random Walk, Normal Distribution, Rayleigh, Maxwell Boltzmann, Diffusion Equation.
belong to the same family of distributions, known as the exponential family of distributions. In this article, we have shown that the random walk can generate Normal, Rayleigh (Chi with 2 DoF) and M-B (Chi with 3 DoF) distributions as its dimensionality increases from 1 to 3. Moreover, as smart