3 ms·
Studying probability right now and seeing how the powerset mobius function immediately implies the inclusion-exclusion formula is pretty cool. Thanks for this!
by carsonlauer 2y ago
Studying probability right now and seeing how the powerset mobius function immediately implies the inclusion-exclusion formula is pretty cool. Thanks for this!
- abelaer 2y agoThe Möbius function actually appears quite often in statistics/probability theory. I wrote more about this in the paper (https://arxiv.org/pdf/2404.14423 https://arxiv.org/pdf/2404.14423), but in short: if you invert moments with the powerset Möbius function then you get central moments, but if you invert moments with the partition Möbius function, then you get cumulants. In fact, you can vastly generalise this by changing the mereology from partitions to ordered partitions etc.