Markov Chains:

Charged particles move circularly in a cyclotron. Assume 3 equal area sectors as shown below.

All particles can reside in a single sector, but generally they are distributed around all three sectors. The states are taken to the sectors: 0, 1, 2. The step size is 1 nanosecond where the percentages of particles in each sector change. The transition diagram is shown below.

(a). Consider the 3 cases where all particles are in only one sector initially. For each case, construct a probability tree taking the initial state (t=0) to t=2 nanoseconds. What are the probabilities of particle distribution in each sector after the 3 nanosecond time period.

(c). If the particles are equally distributed between the three sectors initially, find the % of the particles in sections 0, 1, and 2 after 5 nanoseconds. Is there a time when the distribution becomes steady, i.e. the distribution remains constant after that time?

cyclotron. Assume 3, se below egua 2. 4 ,4 0.2 0.4 do 0.4 0.6 1 2. -0.3 - 0.2- 0.3 - 0.2 cyclotron. Assume 3, se below egua 2. 4 ,4 0.2 0.4 do 0.4 0.6 1 2. -0.3 - 0.2- 0.3 - 0.2