Question: 6. Consider an electronic device that is either on-standby or in-use. The on-standby periods are exponentially distributed with mean of 15 minutes, and the in-use

6. Consider an electronic device that is either

6. Consider an electronic device that is either on-standby or in-use. The on-standby periods are exponentially distributed with mean of 15 minutes, and the in-use periods are exponential with mean of 20 minutes. Since exponential assumption is satisfied, a Markov process with state space E {0,1} can be used to model the device as it alternates between the two states: 0 for on- standby" and 1 for "in-use". a. Justify why the generator of the process will be G= = 01-4 4 113 -3 b. Estimate the probability that the electronic device will be on-standby" after 60 minutes given that it started in-use at time 0. c. In the long run, what is the probability that the electronic device is on-standby? d. Suppose the electronic device costs the company $20 every hour it is in-use and it costs $5 every hour it is on-standby. Find the long run cost per hour for operating the device. 6. Consider an electronic device that is either on-standby or in-use. The on-standby periods are exponentially distributed with mean of 15 minutes, and the in-use periods are exponential with mean of 20 minutes. Since exponential assumption is satisfied, a Markov process with state space E {0,1} can be used to model the device as it alternates between the two states: 0 for on- standby" and 1 for "in-use". a. Justify why the generator of the process will be G= = 01-4 4 113 -3 b. Estimate the probability that the electronic device will be on-standby" after 60 minutes given that it started in-use at time 0. c. In the long run, what is the probability that the electronic device is on-standby? d. Suppose the electronic device costs the company $20 every hour it is in-use and it costs $5 every hour it is on-standby. Find the long run cost per hour for operating the device

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