On the Random Walk Microorganisms Cells Distribution on a Planar Surface and Its Properties

Abstract This paper presents an expansion of the Probability Density Function (PDF) at any time t for the distribution of the microorganism cells movement on the planar surface. A 2-dimensional random walk process accurately models this movement. These cells move linearly on the surface with constant speed and change their direction after exponentially distributed time intervals. In addition, the path length and the uniformly distributed turn angles are independent. Some statistical properties of the original and bounded known version of this distribution have been provided. The estimated length parameter of the cell size is investigated with a simulation study by using a real data set.