A naturalist is observing the behavior of a frog in a small lily pond. There are four lily pads of the pond, and the frog jumps from one to another. The pads are numbered arbitrarily; the state of the system is the number of the pad that the frog is on. Transitions occur only when he jumps. Although he can jump from any pad to any other, the probability of jumping to any given pad fronm the one he is on is inversely proportional to the distance (that is, he is more likely to jump to a near pad than a far one). The distances are: between 1 and 2--6/5 feet between 1 and 3--2 feet between 1 and 4--3/2 feet between 2 and 3--6/7 feet between 2 and 4--1/2 feet between 3 and 4--3/4 feet a. Set up the transition matrix. b. If the frog starts on pad 2, what is the probability that he is on pad 3 two jumps later? c. Interpret the steady-state probabilities in terms of the behavior of the frog. d. Explain in terms of the frog, his motivation, his behavior, and so forth, what the Markov and stationarity assumptions mean.