Compute π (Monte Carlo with Central Limit Theorem)

Project: Compute π (Monte Carlo with Central Limit Theorem)

Write a program that computes and prints π using the Monte Carlo method. See ComputePi2. Compute π 20 times using the Monte Carlo method and take the average to get a better approximation. Use a function to encapsulate the Monte Carlo simulation.

The idea that the average of multiple trials yields a better approximation is called the [[Central Limit Theorem]]. Is this approach any better than just computing one estimate with a larger number of samples?

Output

$ javac -Xlint ComputePi4.java $ java -ea ComputePi4 PI0: 3.141400000000000 PI1: 3.141480000000000 PI2: 3.135720000000000 PI3: 3.149040000000000 PI4: 3.140120000000000 PI5: 3.145400000000000 PI6: 3.150000000000000 PI7: 3.140160000000000 PI8: 3.138680000000000 PI9: 3.136560000000000 PI10: 3.138200000000000 PI11: 3.144160000000000 PI12: 3.147160000000000 PI13: 3.134440000000000 PI14: 3.142960000000000 PI15: 3.135600000000000 PI16: 3.137120000000000 PI17: 3.145680000000000 PI18: 3.139760000000000 PI19: 3.153480000000000 PI: 3.141856000000000 abs(PI - π): 2.6334641021e-04

Solution