Computer Server Down Probability

[iikii]

So the problem asks:

A computer server runs smoothly for Exp(0.2) days and then takes Exp(0.5)days to fix. The server is running fine on Monday morning, t=0. Find the probability that the server was fixed at least once (i.e. at least one complete repair was done) in the next 7 days and the probability that the server was down on Friday t = 4 given that it was running next Sunday t = 6. (W are conditioning on the `future'. )

So do I have to use Markov chain to do this problem? If so, do I need to find out the innitesimal generators to find the probability? I appreciate your insights!

 

[Ray Vickson]

So the problem asks:

A computer server runs smoothly for Exp(0.2) days and then takes Exp(0.5)days to fix. The server is running fine on Monday morning, t=0. Find the probability that the server was fixed at least once (i.e. at least one complete repair was done) in the next 7 days and the probability that the server was down on Friday t = 4 given that it was running next Sunday t = 6. (W are conditioning on the `future'. )

So do I have to use Markov chain to do this problem? If so, do I need to find out the innitesimal generators to find the probability? I appreciate your insights!

Try it and see for yourself. Of course, if you are studying Markov processes in the course, that would be a pretty strong hint.