>>11565356How fucking bizarre. That another person decides to make a thread on the exact same mundane topic as me at near enough exactly the same time.
Jamie is that you?
Also, reposting my question here because relevant:
I'm trying to explain the faulty logic behind the gambler's fallacy in a succinct manner, however currently it sounds pretty janky:
After writing the weak law of large numbers (I wrote it in unicode, cba writing out the latex)
>it can be easily interpreted that if a given number of observations fall below the true mean, then later observations would have to be generally higher than the mean, so that the total observational mean becomes equal to the true mean. This is simply not the case however. In reality, the law regards large numbers of observations; As such, it does not actually apply to any finite subset of observations. Given this, with any finite subset of observations, it is impossible to infer any information about other subsets or super-sets.I'd like to try and set that up formally with the proper notation, but i'm not sure the best way to go about it.
This obviously seems trivial: it seems like i'm trying to prove that a random variable is i.i.d, when we already assume its i.i.d as part of the setup. But rather i'm trying to get across the rational of why we can't make observational inferences about other elements in an infinitely large set.
My general idea was, in abstraction (again, sorry for the poor formatting):
>Take an i.i.d random variable R with Sample Space S>Subsets A and B, where A is a subset of B, and B is a subset of S.>???>proof that the mean of subset B is independent of the mean of R and A.Obviously, the way i'm presenting it is wrong, I think in both terms of terminology and overall approach. What would be the best way to formalise my point?
