2. Consider the following scenario: a If a trafc light is green, it stays green 70% of the time, and otherwise it turns yellow. 0 If a trafc light is yellow, it stays yellow 5% of the time, and otherwise it turns red. 0 If a trafc light is red, it stays red 25% of the time, and otherwise it turns green. (a) Draw a transition diagram for a Markov chain that captures the above scenario. Label the states and transition probabilities ap- propriately. (b) Write down the one step transition matrix for this Markov chain. (c) If you start at a red light, what is probability that after two steps, the light will be green? Show your working