Random Walk, Normal Distribution, Rayleigh, Maxwell Boltzmann, Diffusion Equation.
the Chi distribution. np.random.seed(1) N, M = 1000000, 1000 x = np.random.binomial(1, 0.5, size=(N, M)) x[x==0] = -1 y = np.random.binomial(1, 0.5, size=(N, M)) y[y==0] = -1 # Distance from the origin to the final destination r = ((np.sum(x, axis=0)/1000)**2 + (np.sum(y, axis=0)/1000)**2)**0.5