Information geometry (Geometry and Nature) has emerged from the study of invariant properties of the manifold of probability distributions. It is regarded as mathematical sciences having vast developing areas of applications as well as giving new trends in geometrical and topological methods.
Information geometry has many applications which are treated in many different branches, for instance, statistical inference, linear systems and time series, neural networks and nonlinear systems, linear programing, convex analysis and completely integrable dynamical systems, quantum information geometry and geometric modelling.
Here, we give a brief account of information geometry and the deep relationship between the differential geometry and the statistics[1,4,5,10,11].The parameter space of the random walk distribution using its Fisher's matrix is defined. The Riemannian and scalar curvatues of the parameter space are calculated. The differential equations of the geodesic are obtained and solved. The relations between the J-divergence and the geodesic distance in that space are found.