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The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given year 70 % of programmers remain in that position 20 % are promoted to project manager and 10 % are fired (state X). 95 % of project managers remain in that position while 5 % are fired. How long on the average does a programmer work before they are fired?

Solved it through the transition matrix where the equations are, m(P) = 1+ 0.7 m(P) + 0.2 m(M) m(M)= 1 + 0.95 m(M) So m(M)= 20, and m(P)= 16.67,

I hope someone can confirm this. Thank you

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    $\begingroup$ Perhaps you should explain and justify in detail (not winging it) how you determined these equations, and how their solution provides the solution to the question asked. $\endgroup$ Mar 17, 2018 at 21:12
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    $\begingroup$ You should also try another method, such as evaluation of the probability of being fired in n steps for n from 1 up to a large enough number, by computing the n step transition matrix. Then use these values to compute the expected number of steps (years) until firing. $\endgroup$ Mar 18, 2018 at 1:33

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Since there are no cycles in the career path, you can simply use the geometric distribution to work out how long people stay in their respective positions:

  • Programmers stop with probability $p=0.3$ after each year, so stay programmers for $1/p = 10/3$ years on average

  • Project managers are fired with probability $p=0.05$, so say in their job for $1/0.05 = 20$ years on average.

Thus, the average length of a programmer's career seems to be $10/3 + 2/3 * 20 = 16.67$. So I'm siding with you on this one.

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