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In: Statistics and Probability

Perimeter Road has 4 streetlights. A streetlight burns out after an average of 100 days of...

Perimeter Road has 4 streetlights. A streetlight burns out after an average of 100 days of use (exponentially distributed). It takes an average of 10 days to replace a burned-out street lamp (exponentially distributed). Model the number of functioning streetlights as a birth-and-death process.

(a) What is the long-run proportion of time that all streetlights are burned out?

(b) On average how many streetlights are illuminating the Perimeter Road?

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orchestra answered 2 years ago
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