CS 4960 Fall Semester 1999

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  Problem 9-1

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  Assigned: 21 October 1999 Due: 2 November 1999  
 
Design and run a simulation study to anaylze the use of Monte Carlo techniques.  Calculate the integrals given below using both the average of values approach as well as the area of volume approach. Study the confidence of the answers in terms of the variance, the stdev error estimate versus number of trials, etc.  See what general conclusions you reach in terms of the applicability of the techniques.
 

• Integral{0,pi} sin(x)dx
• Integral{volume defined in handout} torus_intersection_with_box
• Calculate pi using 1/4 of unit circle