Please set up a Markov Chain:

3. Compartments] Random Particle Movement Model (35 total points) In a physics experiment a particle is placed in Chamber A of the space shown below. The scientists observe the length of time for the particle to rst enter the special chamber, ghamber F, where time is measured by the number of chambers the particle visits. For example if the particle starts in Chamber A and proceeds to Chamber D and then to E and then to F, then the length of time to go from A to F is 3. Assume that the particle will move in a random way belmcing off the walls the chamber that it is currently in until it randomly exits the current chamber through any available opening out of a chamber with equal likelihood. For example, if there are two openings available in a particular chamber then the particle will eventually exit this chamber by either of the openings with equal probability. [In counting the openings, include the one that the particle used to enter the chamber because the particle could retrace its steps.) Note: When the particle enters Chamber F [or C} it will leave Chamber F [or C) 1via the only opening possible and re-enter Chamber E (B). Figure 2: lCompartmental Random Particle Movement Model In this picture there is only an opening if there is a gap in the lines indicating a wall. (a) (5 points) Model the particle's journey through the system to the special chamber, Chamber F, as a Markov Chain and write the single-step transition matrix {complete with numbers). You must also write how you specify the initial state