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Toss a fair coin N times. Does the number of the same side appearing in a row converge to a finite number? If yes, what is it in terms of N? Are confidence intervals needed? Thank you!

Bende
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  • i did not understand. can you please explain with an example? – gt6989b Jan 31 '17 at 20:20
  • This is not at all clear. Please define precisely what you are trying to calculate. If possible, give an example for $N=3$ say. – lulu Jan 31 '17 at 20:25
  • Okay! I meant the following. Let me do it with a greater N, say N=100. So when I toss the fair coin 100 times, what can I say about the longest HEADs in a row? That is With 95% confidence I can say that there will be no longer HEADs after each other than say 10. So the sequence would be: {H,T,T,T,H,H,T,H,WHATEVER,...,HHHHHHHHHH,T,...,LAST} – Bende Jan 31 '17 at 20:32
  • And so the larger N goes, there will be more likely to observe "long" rows of the same side, say HEAD. Example: N=100,000, there will be 15 HEADs in a row. – Bende Jan 31 '17 at 20:36
  • Because I was playing around with excel, and as I have increased N, the longest row of the same side was not increasing by the same factor as N did. Hence, I thought it might converge to a finite number. But then it is still a random process so confidence intervals might be useful to introduce to the picture. – Bende Jan 31 '17 at 20:38
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    this question is relevant. As is this one – lulu Jan 31 '17 at 20:44

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