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Suppose a businessman has 3 mobile phones, each of which independently lasts for an exponentially distributed...

Suppose a businessman has 3 mobile phones, each of which independently lasts for an exponentially distributed time with a mean of 4 months. Let X(t) be the number of these phones that have broken down after T months.

(a) Model (X(t),t ≥ 0) as a pure birth process by giving the state space and birth rates.

(b) What is the probability that all 3 phones are still working after a half month?

(c) On average, how long will it take before there is only one working phone left?

Math   Statistics-And-Probability   
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