2. 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 negative exponentially distributed. That is, if no melting were to occur, the time until one more inch would fall would be negative 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 chang- ing depth of snow on the ground in inches. Provide a transition diagram or matrix and identify all parameters.
2. 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 negative exponentially distributed. That is, if no melting were to occur, the time until one more inch would fall would be negative 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 chang- ing depth of snow on the ground in inches. Provide a transition diagram or matrix and identify all parameters.
Chapter10: Exponential And Logarithmic Functions
Section10.5: Solve Exponential And Logarithmic Equations
Problem 10.88TI: Researchers recorded that a certain bacteria population declined from 700,000 to 400,000 in 5 hours...
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Transcribed Image Text: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 three inches of snow on the ground.
Transcribed Image Text:2. 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 negative exponentially distributed. That is, if
no melting were to occur, the time until one more inch would fall
would be negative 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 chang-
ing depth of snow on the ground in inches. Provide a
transition diagram or matrix and identify all parameters.
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