a. A taxi cab driver in New York City is driving around aimlessly looking for work. If the driver turned left at the last intersection, then he will not turn right at this intersection, and there is a % probability that he will go straight. If the driver went straight through the last intersection, then he will not go straight through this one1 and he is equally likely to turn left or right. If he turned right at the last intersection, then he will not tum left at this one, and he is 3 times more likely to turn right again than he is to go straight. Draw the transition diagram, and nd the corresponding transition matrix. b. A cat has 3 activities: eating, sleeping, and going outside. If the cat is eating on one observation, it will not be eating on the next observation, and is equally likely to he asleep or outside. If the cat is sleeping on one observation it will not be outside on the nmt observation, and is twioe as iikely to he asleep as it is to be eating. If the cat is outside on one observation, then it will not be eating on the next observation, and the probability that it will be sleeping is %. Draw the transition diagram, and nd the corresponding transition matrix. . If you chose a or b in the previous problem, then choose the same part for this problem. a. Suppose the taxi cab driver goes straight through the 1st intersection. [a] Find the probability that he goal straight through the 3rd intersection. {b} Find the probability that he turns left at the next 3 intersections. b. Suppose the cat is sleeping on the lat observation. [a] Find the probability that it is sleeping on the 3rd observation. {bl Find the probability that it alternates between sleeping and eating for the rst 4 observations