Renewal-reward fraction of time running

MediumExpected Value Stochastic Processes~4m

A machine runs for an $\text{Exp}(\text{mean }4\text{ hours})$ cycle, then takes exactly $1$ hour to reset, repeatedly. In the long run, what fraction of time is it running? (to 3 decimals)

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Use the renewal-reward long-run fraction.
Fraction = $E[\text{run}]/(E[\text{run}]+E[\text{reset}])$ .

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0.8 (± 0.005)

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Renewal-reward fraction of time running

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