# Name of this discrete stochastic process

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?

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