4. Do one of the following two problems. n. A taxi cab driver in New York City in driving around aimlessly looking for work. If the driver turned left at the last intersection, then be will not turn right at this intersection, and there is - probability that be will go straight. If the driver went straight through the bat intersection, then he will not go straight through this one, and he is equally likely to turn left or right. If he turned right at the bat interaction, then be will not turn left at this one, and he is il times more likely to turn right again than he is to go straight. Draw the transition diagram, and find the corresponding transition matrix. b. A cat has 1 activities: cating, sleeping, and going outside. If the cat is cating on one ohaccretion, it will not be cating on the next observation, and is equally likely to be askap or outside. If the out is sleeping on one observation it will not be outside on the next observation, and is twice in likely to be asleep as it is to be eating. If the cut is outside on one observation, then it will not be cating on the next observation, and the probability that it will be sleeping is }. Draw the transition diagram, and find the corresponding transition matrix. 5. If you choose a or & in the previous problem, then choose the same part for this problem. i. Suppers the taxi cab driver goes straight through the Ist intersection. (a) Find the probability that he goes straight through the ard intersection. (b) Find the probability that he turns left at the next 3 interactions. b. Support the eat is sleeping on the lat observation. (a) Find the probability that it is sleeping on the iled observation. (b) Find the probability that it alternates between sleeping and cating for the first 4 cheerstions