Suppose you have an alternating renewal process: A new machine begins
operating at time 0 and breaks down after a random amount of time whose
distribution is F1. It takes a random amount of time whose distribution is
F2 to replace the broken machine with a new machine with characteristics
identical to the original. Successive periods are independent and alternate
between having distributions F1 and F2.
Dene fx(t) to be the probability that at time t there is an operating machine
and that it stays operative for at least x more time units. In what follows,
x is always xed.
(i) Write the renewal equation satised by fx(t).
(ii) Solve the equation.
(iii) Compute limt!1 fx(t).
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