Question: A small company has three trucks that break down often. It has been observed that if all the threetrucks are working in the morning, there
A small company has three trucks that break down often. It has been observed that if all the threetrucks are working in the morning, there is 10% chance that all the three trucks fail by the evening,25% chance that two trucks fail by the evening while there is 30% chance that only one fails by theevening. However, if two trucks are working in the morning, then there is 30% chance that one failswhile 20% chance that two fail by the evening. If only one truck is working in the morning, thenthere is 45% chance that it fails by the evening. If a truck fails during the day, the truck is taken tothe companys garage to repair. Assume that it takes one day to repair a truck regardless of howmany trucks are in the garage (i.e., even if all the three trucks are broken down, it takes one day torepair all the three trucks). Letting the state of the system be the number of trucks working in themorning, construct one step transition matrix assuming that the Markovian property along withstationary increment properties hold for the corresponding stochastic process.
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