3 ms·
> a random stream of bits should have almost as many ones as zeros almost??
by flir 3y ago
> a random stream of bits should have almost as many ones as zeros
almost??
- xvedejas 3y agoI think this is the correct way to phrase it. Just because the probabilities of each are both 50% doesn't mean it's more likely than not to get the same number of ones and zeros. It would just mean you're equally likely to get a few more ones as you are to get a few more zeros. But the counts are unlikely to be very far apart.
- 082349872349872 3y agoBut in absolute (not relative terms) the counts will tend to diverge over time.
- eru 3y agoYes. You expect the absolute difference in numbers of 0s vs 1s to grow roughly with the square-root of the total number of digits produced.
- philipswood 3y agoIn the limit, yes. But for the first few bits maybe "almost".
- thisisauserid 3y agoYou aren't suggesting that something random should be predictable, right?
- 0xFF0123 3y ago"Almost" suggests it is predictably fewer
- AlecSchueler 3y agoIt suggests roughly the same amount, could be higher or lower.
- deleted 3y ago[deleted]
- niles 3y agoAround would do that more effectively. Almost is more similar to nearly, and I agree commonly used for lower.
- KTibow 3y ago"Around" might be better
- flir 3y agoI read "almost as many" as "not quite as many". In other words, fewer. My mental model is that an unbiased random stream of 1's and 0's should converge on 50% 1's and 50% 0's over time, not 49% 1's and 51% 0's. Looks like it's a language ambiguity thing I'm not quite getting.
- madeofpalk 3y agoTo converge on 50% implies 49%\51% prior. Almost even.
- ruune 3y agoOver time, it should be almost 50/50, yeah. What if you got 10000001 random numbers? There's no way it's exactly 50/50 with an uneven amount. It's almost 50/50
- deleted 3y ago[deleted]
- b112 3y agoYes, almost. They will approach equal as the count approaches infinity. So if ypu ever see a random pick equate to 50/50, the end of the universe is upon us.
- eru 3y agoThe ratio of occurrences of 0s and 1s will go to one in the limit. But the absolute difference of occurrences will diverge. (It grows roughly like the square-root of the number of digits.)
- AlexAltea 3y agoNit, their ratio (bits set/unset) will approach 1 as the count approaches infinity, but the values themselves will not approach equal. https://gist.github.com/AlexAltea/3aa96efc41f59e80631c346908fe8ed5 https://gist.github.com/AlexAltea/3aa96efc41f59e80631c346908...
- alex_smart 3y agoWith n random bits, you will likely have approximately \sqrt{n} more ones than zeros (or vice versa).
- Rebelgecko 3y agoIf a random streams length is odd, they'll never be the exact same.