You are flipping n fair coins, putting aside those that come up heads after each flip. What's the expected number of rounds?

Asked Apr 13 '19 at 15:01

Active Nov 13 '20 at 22:00

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This question is related to https://www.quora.com/You-are-flipping-100-coins-putting-aside-those-that-come-up-heads-after-each-flip-How-many-flips-do-you-expect-to-make-before-running-out-of-coins-to-flip

At each stage, you flip all your coins and only keep the ones that are tail. You stop when you ran out of coins. Some Quora answers mention that the expected number of rounds is logarithmic with respect to $n$. Any suggestions on how you would prove this fact?

edited Apr 13 '19 at 18:44

asked Apr 13 '19 at 15:01

johndoe8971

Possible duplicate of Expectation of the maximum of i.i.d. geometric random variables – Mike Earnest Apr 13 '19 at 17:28
How are the two problems the same? – johndoe8971 Apr 13 '19 at 18:03
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Let $X_i$ be the number of rounds the $i^{th}$ coin survives for. The $X_i$ are i.i.d. geometric, and you want the maximum of the $X_i$. – Mike Earnest Apr 13 '19 at 18:32

You are flipping n fair coins, putting aside those that come up heads after each flip. What's the expected number of rounds?

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