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Why are the waiting times in these states exponentially distributed? (Practice question 4.6)

M

M Willis

Active Member
In question 6 of the chapter 4 summary questions for CS2, the following scenario is given:

In a particular company the salary scale has only two different levels. On average, an employee spends 2 years at level 1 before moving on to the higher level, or leaving the company. An employee at the maximum level spends an average of 5 years before leaving. Nobody is demoted, promotion can occur at any time, and mortality can be ignored.
Upon leaving level 1, the probability that an employee moves to level 2 is 50%.
Click to expand...

In the solution to part iii of this question, which asks you to find the generator matrix of the process, it states that the ‘average waiting time in each state, i is exponentially distributed’.

Could someone explain to me why this is necessarily true (as far as I can tell this was not specified in the question)?
 
The waiting times in a TH MJP are always exponentially distributed. See p30 of Ch4.
 
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