3. (The Ehrenfest diffusion model) The Ehrenfest model is a basic model used in physics. There are N particles moving randomly in a container divided into two halves - A and B (see Figure 1). We consider the number of particles in the left and right halves of the container. At every discrete time step, a randomly chosen particle moves to the other half of the container it is currently located in. Let Xn be the number of particles after n time steps on the left half of the container (Box A in the figure). Box A Box B nt N-nt 08 8 Figure 1: Ehrenfest Diffusion Model (c) Suppose that the initial distribution for the initial number of black balls X, is Binomial (N, 1/2). Find the distribution of X 100- 3. (The Ehrenfest diffusion model) The Ehrenfest model is a basic model used in physics. There are N particles moving randomly in a container divided into two halves - A and B (see Figure 1). We consider the number of particles in the left and right halves of the container. At every discrete time step, a randomly chosen particle moves to the other half of the container it is currently located in. Let Xn be the number of particles after n time steps on the left half of the container (Box A in the figure). Box A Box B nt N-nt 08 8 Figure 1: Ehrenfest Diffusion Model (c) Suppose that the initial distribution for the initial number of black balls X, is Binomial (N, 1/2). Find the distribution of X 100