Suppose we have $n$ blocks of wood. At each step, we choose one of these boxes uniformly at random and paint it red (so at later steps, we may be re-painting an already-red box). Let $X_t$ denote the percentage of the boxes painted red at time $t$.

In other words, take $X_0 = 0$ and let

$X_{t+1} = \begin{cases} X_t & \text{ with probability } X_t \\ X_t + 1/n & \text{ with probability } 1 - X_t \end{cases}$

Question: What is the name of this process?

  • $\begingroup$ Certainly looks like a Markov chain. Not sure if there is a specific name though. $\endgroup$ – gt6989b Jul 9 '12 at 20:55

This should go in a comment, but it looks to me like a coupon-collector problem. http://en.wikipedia.org/wiki/Coupon_collector's_problem

  • $\begingroup$ Since I just asked for the name, this is a perfectly good answer! $\endgroup$ – Daniel McLaury Jul 9 '12 at 22:14
  • $\begingroup$ Just be careful with the way you defined your process, you might have to adapt if you want to do any sort of calculation. But you can definitively relate to the C-C problem $\endgroup$ – Jean-Sébastien Jul 9 '12 at 22:29

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