μandthenfails. a repair crew checks the machine at times distributed according to a poisson process with rate λ; if the machine is found to have failed then it is immediately replaced. find the expected time between replacements of machines.

Step-by-step explanation:

If a machine is replaced at some time t, then the expected time until next failure is

and the time between the checks is exponentially distributed with rate \lambda, the expected time until next failure is  

Because of memory less property of the exponential  The answer is