Assignment:
Consider a city of 500,000 people, whose inhabitants have been classified by the authorities as either “not criminal,” “misdemeanor,” or “felon.” Long-term studies indicate that the transition of an individual from one state to another from 1 year to the next is shown in the transition matrix
City council contemplates a new program that costs $70,000,000 and changes the transition probabilities to
Assume that an individual in the “misdemeanor” category costs about $1,000 annually, while the cost of a felon are $10,000 each year.
(a) What is the probability that a felon does not commit any crime in the next 2 years with and without the crime prevention initiative?
(b) What is the probability that an individual in the “misdemeanor” category does not commit any crime in the next 3 years with and without the crime prevention initiative?
(c) What are the steady state probabilities with and without the initiative? Compare the long-term costs with and without the initiative.
(d) What are the mean recurrence times for the three categories with and without the incentive? How many years, on average, does it take for an individual to move from the “felon” to the “misdemeanor” category, without the crime prevention initiative?
Provide complete and step by step solution for the question and show calculations and use formulas.