Consider 4 iPhones, each independently having a battery lifetimethat is exponen-

Question

Consider 4 iPhones, each independently having a battery lifetimethat is exponen-
tially distributed with mean 1:25 years (hence rate =1=(1:25) = 0:8). Once a
battery breaks down, the iPhone immediately goes to a facility tohave the battery
replaced. The replacing facility nearest you handles only the above4 phones (no
others), but can only work on 1 phone at a time (the others wait inqueue). Replac-
ing times are exponentially distributed with mean 0:01 year (hencerate = 100.).
Let X(t) denote the number of iphones at time t that have workingbatteries. Ar-
gue thatfX(t)g forms a continuous-time Markov chain. Give theholding time rates
a0; a1; a2; a3; a4, and the transition probabilities Pi;j for theembedded discrete-time
Markov chain.

Explanation / Answer

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