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« on: October 10, 2020, 06:21:40 pm »
Wow, this was reaaaallly hard for me to accept.
I was also thinking that the ~2.72 MUST HAVE BEEN due to the way qb64 creates a RANDOM number.
After a couple of tests, I realize my idea of how random numbers add up WAS wrong, and so I thought I'd share.
examining the sum of 3 random numbers,
I was thinking that adding 3 random numbers, where each random number has an equal distribution between 0 and 1,
would create a probability distribution space ranging between 0 and 3 equally, which would imply that the probability of the sum of 3 random numbers
adding up to less than 1 would simply be 1/3, which is WRONG because that is equivalent to thinking that the sum of 3 random numbers is on average equal to 1
random number x 3, which is a fallacy!
the volume boundaries you attached explain well how to properly understand the sum of random numbers by accepting that each
random number deserves it's own dimension and that the probability of the sum of n random numbers less than 1 is indeed equal to 1/n!
very beautiful to see Euler's number appear here as the sum of probabilities. Thanks for updating my view on numbers STxAxTIC!