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

$ python3 ComputePi4.py PI0: 3.149200000000000 PI1: 3.137680000000000 PI2: 3.151600000000000 PI3: 3.135200000000000 PI4: 3.136480000000000 PI5: 3.139960000000000 PI6: 3.146200000000000 PI7: 3.143160000000000 PI8: 3.146160000000000 PI9: 3.144480000000000 PI10: 3.136920000000000 PI11: 3.142720000000000 PI12: 3.141520000000000 PI13: 3.139760000000000 PI14: 3.148720000000000 PI15: 3.135240000000000 PI16: 3.140120000000000 PI17: 3.138040000000000 PI18: 3.132840000000000 PI19: 3.138960000000000 PI: 3.141248000000000 abs(PI - π): 3.4465358979e-04

Solution