A (very) minor league baseball player has a history of injuries which is limiting his career potential. His status varies between three states: 1 (healthy), 2 (minor injury but able to play), and 3 (major injury preventing competition). The team doctor has a bachelor's degree in industrial engineering and concluded that the transitions between states could be modeled using the embedded Markov chain with transition matrix P = [ 0 1 4 3 4 1 3 0 2 3 1 0 0 ] Sojourn times in states 1, 2, and 3 are exponentially distributed with average times of 1/3, 1/4, and 1/5 days respectively. Let X(t) be the continuous time Markov chain describing the state of the player at time t days. (a) Determine the transition rate matrix for the continuous time Markov chain and draw its transition diagram. (b) What proportion of time in the long run will the player be able to play? (c) What is the expected time for a player to get injured and miss the competition for the first time, given that he is currently healthy? (d) What is the expected time for a player to return from a major injury if he is currently