Monte Carlo Integration
Problem Set
Solutions
Output using default seed:
CORRECT ANSWER: 1.33333 UNSTRATIFIED UNIFORM RANDOM SAMPLING: 1.35031 STRATIFIED UNIFORM RANDOM SAMPLING: 1.33284 STRATIFIED IMPORTANCE SAMPLING PROPORTIONAL TO X^2: 1.16347 STRATIFIED IMPORTANCE SAMPLING PROPORTIONAL TO (M_PI/2 - X)^2: 1.14893 STRATIFIED IMPORTANCE SAMPLING WITH (PDF1 + PDF2)/2: 1.33422 Press Enter to continue!
Output using srand48(1934):
CORRECT ANSWER: 1.33333 UNSTRATIFIED UNIFORM RANDOM SAMPLING: 1.31934 STRATIFIED UNIFORM RANDOM SAMPLING: 1.33317 STRATIFIED IMPORTANCE SAMPLING PROPORTIONAL TO X^2: 1.43007 STRATIFIED IMPORTANCE SAMPLING PROPORTIONAL TO (M_PI/2 - X)^2: 1.1179 STRATIFIED IMPORTANCE SAMPLING WITH (PDF1 + PDF2)/2: 1.33322 Press Enter to continue!