Those interested in this should read about DSMC: https://en.wikipedia.org/wiki/Direct_simulation_Monte_Carlo. It’s the same idea for low density gas interactions without having to actually simulate all the particles involved while still getting accurate results. Cool stuff!
There's been a lot of interesting work in the last ~decade on improving monte-carlo methods for solving PDEs, the field is really fascinating!
> After running 10 million simulated draws, I got an answer of 0.0323, which matches the real answer very closely.
If you enjoyed reading about how you can approximate complex statistical values using basic programming, I highly recommend Jake Vanderplas "Statistics for Hackers" [0][1].
It converts the sometimes hard to grok statistics terms and formulas into some very simple loops and basic operations.
Can't recommend it enough.
0 - https://speakerdeck.com/pycon2016/jake-vanderplas-statistics...
> Can't differentiate the function? Fuck gradients. Here's the entire fucking posterior.
- Monte Carlo