Problem 2: ears between three states: 1 (bankruptcy), 2 (verge of uctuates in successive y ' cess is Jim's restaurant business S; . _ Markov transition matrix of this pro bankruptcy), 3 (solvency). The 1 0 0 P: 0.5 0.25 0.25 (1) 0.25 0.25 0.50 Assume the maximal lifetime of a restaurant is T = 50 years. Sample size N = 2000. (a) [2pts] Let X be the stopping time from the initial solvency, i.e., the years until Harry's restaurant goes bankrupt assuming he starts from the state of solvency So = 3. Plot the histogram of X and compute its 95% condence interval. if (b) [2pts] Let K be the stopping time when the restaurant is initially on the verge of bankruptcy (50 = 2). Plot the histogram of K and compute its 95% condence interval. (c) [2pts] Does initial state matter in the restaurant business? Why or why not? Make your case based on the results from (a)-(b). ((1) 12pm] What is the distribution of the restaurant's state in year 50, ST, with initial state solvency, i.e. , the probability of the restaurant in states 1, '2, 3, respectively? And the distribution with initial state 30 = 2'