Example During the winter months in a particular city, snowfall occurs at the average rate of two inches per week. Melting and evaporation will reduce existing accumulation at the rate of three inches per week. In both cases, the time in days to increase or decrease an inch is exponentially distributed. That is, if no melting were to occur, the time unit one more inch would fall would be exponentially distributed. Similarly, if there were no new snow, the time to decrease an inch would be exponential. Of course, both natural processes occur together. a) Develop a continuous time Markov model of the changing depth of snow on the ground in inches. Provide a transition diagram and identify all parameters. b) Is the Markov assumption reasonable? Discuss factors that would tend to affirm or refute the assumption. (Don't worry about stationarity.) c) Show how to compute the fraction of time there is more than and equal to three inches of snow on the ground. Example During the winter months in a particular city, snowfall occurs at the average rate of two inches per week. Melting and evaporation will reduce existing accumulation at the rate of three inches per week. In both cases, the time in days to increase or decrease an inch is exponentially distributed. That is, if no melting were to occur, the time unit one more inch would fall would be exponentially distributed. Similarly, if there were no new snow, the time to decrease an inch would be exponential. Of course, both natural processes occur together. a) Develop a continuous time Markov model of the changing depth of snow on the ground in inches. Provide a transition diagram and identify all parameters. b) Is the Markov assumption reasonable? Discuss factors that would tend to affirm or refute the assumption. (Don't worry about stationarity.) c) Show how to compute the fraction of time there is more than and equal to three inches of snow on the ground