3 ms·
General statistical question. If we say extend the coin flip example distribution to say 10B times. Should/would we expect to see a streak of 100 or even 1000
by indigodaddy 1y ago
General statistical question. If we say extend the coin flip example distribution to say 10B times. Should/would we expect to see a streak of 100 or even 1000 in the distribution somewhere? Intuition alone tells me probably not for 1000 but a smallish chance for 100 (even if 10B in a row i would think a streak of 100 would be unlikely)
- steppi 1y agoYour intuition's not bad. The expected value for the longest run of heads in N total flips of a fair coin is around log2(N) - 1 with a standard deviation that's approximately 1.873 plus a term that vanishes as N grows large. log2(10B) - 1 is approximately 32 and with that standard deviation, even a run of 100 in 10B flips is incredibly unlikely. For more info see Mark F. Schilling's paper, "The Longest Run of Heads" available here https://www.csun.edu/~hcmth031/tlroh.pdf https://www.csun.edu/~hcmth031/tlroh.pdf.
- xrisk 1y agoThat’s a cool result, thanks for the link!
- indigodaddy 1y agoNeat! I guess this is a common thing to wonder about :)