Help with the problem. Please show steps for each question

4. Consider a stock which always sells for $10, $20, or $30. If it is selling for $10 today, there is a 0.7 chance that it will sell for $10 tomorrow and 0.2 chance that it will sell for $20 tomorrow. If it is selling for $20 today, there is a 0.6 chance that it will sell for $20, and 0.3 chance for $10 tomorrow. If it is selling for $30 today, there is a 0.5 chance that it will sell for $30, and 0.1 chance for $10 tomorrow. (a) (4) Give the state diagram. (b) (5) In the long run, what is the average stock price? (c) (5) What is the mean first passage time for the stock to increase from $10 to $20? (d) (5) If this stock is selling for $10 today, what is the probability that the stock is selling at $20 two days later? (e) (3) Is the following Markov chain ergodic? Why? 0.5 0 0 0.5 0.2 0.2 0.2 0.4 0.6 0 0.2 0.2 10.1 0.1 0 0.8) 4. Consider a stock which always sells for $10, $20, or $30. If it is selling for $10 today, there is a 0.7 chance that it will sell for $10 tomorrow and 0.2 chance that it will sell for $20 tomorrow. If it is selling for $20 today, there is a 0.6 chance that it will sell for $20, and 0.3 chance for $10 tomorrow. If it is selling for $30 today, there is a 0.5 chance that it will sell for $30, and 0.1 chance for $10 tomorrow. (a) (4) Give the state diagram. (b) (5) In the long run, what is the average stock price? (c) (5) What is the mean first passage time for the stock to increase from $10 to $20? (d) (5) If this stock is selling for $10 today, what is the probability that the stock is selling at $20 two days later? (e) (3) Is the following Markov chain ergodic? Why? 0.5 0 0 0.5 0.2 0.2 0.2 0.4 0.6 0 0.2 0.2 10.1 0.1 0 0.8)