Mathematics: 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.

0.35 as a decimal and 7/20 for the fraction....

μandthenfails. a repair crew checks the machine

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11.01.2022

$\frac{1}{\mu }+\frac{1}{\lambda }$

Step-by-step explanation:

If a machine is replaced at some time t, then the expected time until next failure is $\frac{1}{\mu }$

and the time between the checks is exponentially distributed with rate \lambda, the expected time until next failure is $\frac{1}{\lambda }$

Because of memory less property of the exponential The answer is

$\frac{1}{\mu }+\frac{1}{\lambda }$

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