## 2001 Term Project

### Due: Friday, December 14, 2001 @ 17:00

#### What you need to turn in to complete this project:

1. A précis of your work—include a description of the algorithm (s) you use and the structure of your program. This is the place to discuss any difficulties you might have encountered.
3. Output from representative runs.
4. Your results, in tabular form, including any (optional) graphical representations you might wish to include. Since this is Monte Carlo, estimate the statistical uncertainty of your answers.

#### The problem:

Pretend you are a criminal who must choose among different types of crimes. The justice system provides a probability qk that if you commit the k'th type of crime you will be caught and punished. Each kind of crime has a distribution of sentence length,

pk(J)=4Jexp[–2J/j k]/(jk)2

where jk is the average sentence for each kind of crime. That is, if you are caught for crime k you will receive a sentence of length J years with probability pk(J)dJ. On the other hand, you receive a payment mk for each successful crime.

Capture and sentencing parameters
Category of crime

q

j
(years)
m
(dollars)
larceny 0.05     2    50
robbery 0.1     4   100
burglary 0.15     6   500
arson 0.25    10  1000

In a time dt you can commit Rkdt crimes of type k, gaining profit

dPk=(1-qk)mk Rkdt.

Of course you could go to jail, in which case your personal clock is advanced by J years.

Your task is to find values of Rk that will yield you at least \$16,000 total profit per year and that will maximize your lifetime earnings (by minimizing the total time you spend in jail).