Please note that the transition RATE matrix is not given, it must be found, but it is nessesary to solve B, C, and D. So please make sure that A is correct.

(I have no idea what you mean by reference, this is all the info given for the problem)

(50pts) 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=0311410043320 Sojourn times in states 1,2 , and 3 are exponentially distributed with rate of 31 per day, 41 per day, and 51 per day , 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. (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 major injured for the first time, given he is currently healthy? (d) What is the expected time for a player return to major injured if he is currently major injured