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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 32 / 2 / b

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2014 iii Paper 32 2
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b
In a time-homogeneous continuous-time Markov chain, a state's holding time is exponential with rate equal to its total outgoing transition intensity. Converting the specified times to months gives
a+b=961​,a+ba​=21​,c=361​.
(1)
The exit-type probability follows by dividing its transition intensity by the total exit rate. Therefore
a=b=1921​,c=361​,Q=​−1/9600​1/192−1/360​1/1921/360​​ month−1.​
(2)
These are starting values for numerical estimation, rather than further observations or constraints on the final fitted rates.

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