17. An employee's morale describes the feelings of enthusiasm and loyalty the employee has about their work and their employer. It is common to classify an employee's morale as high, neutral, or low. A company is said to have a serious morale problem if, typically, more than 10% of employees have low morale. We are interested in determining whether or not a particular company, Company X, has a serious morale problem. No available data describes how employees currently feel. However, recently collected data suggests the following heuristics for how morale at Company X changes each day: 0 of the employees with high morale today, 94% will have high morale tomorrow and 5% will have neutral morale tomorrow; 0 of the employees with neutral morale today, 6% will have high morale tomorrow and 90% will have neutral morale tomorrow; 0 of the employees with low morale today, 1% will have high morale tomorrow and 7% will have neutral morale tomorrow. (a) Draw a diagram for a Markov Chain model that describes how the morale of a randomly selected employee at Company X changes between State 1: High morale, State 2: Neutral morale, State 3: Low morale. (b) Write down a stochastic matrix T for a Markov Chain model that describes how the morale of a randomly selected employee at Company X changes between State 1: High morale, State 2: Neutral morale, State 3: Low morale. (c) Suppose that T is the matrix from part (b) and ED, 531, 532, . . . is a sequence of probability vectors in R3 such that EH1 2 Tip, for k: = 0, 1,2, . What do the entries in 57';- represent? 52/129 ((1) A computation determines that q' = 47/ 129 is a steadystate of the matrix T 30/129 from part (b) Using this information, say what you can about employee morale at Company X