(Same subject as [15.073[J]](http://student.mit.edu/catalog/m15a.html#15.073), [IDS.700[J]](http://student.mit.edu/catalog/mIDSa.html#IDS.700)) Prereq: 6.041B or [18.600](http://student.mit.edu/catalog/m18b.html#18.600) A vigorous use of probabilistic models to approximate real-life situations in Finance, Operations Management, Economics, and Operations Research. Emphasis on how to develop a suitable probabilistic model in a given setting and, merging probability with statistics, and on how to validate a proposed model against empirical evidence. Extensive treatment of Monte Carlo simulation for modeling random processes when analytic solutions are unattainable.