Question: 1. (25 total points) For Question 1, consider the four-state CTMP that has rate diagram as given, and measures time in hours. Initially the process

1. (25 total points) For Question 1, consider the four-state CTMP that has rate diagram as given, and measures time in hours. Initially the process is in State 3. 13.5 3.3 (a) (5 points) Write the corresponding state-transition rate matrix, A. (b) (5 points) If the process has been in State 1 for to hours, write the mean length of time before leaving State 1. (c) (5 points) If the process has been in State 1 for hours, state the probability that the next state to be visited is State 4. (d) (5 points) Compute P(X (1) = 1X (0) = 1). (Remember to show your work, any formulae used, and/or MATLAB code)

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