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The question is similar to exercise 5.5.1 in Probability: Theory and Examples 5th edition by Durrett.

Let $\xi_1, \xi_2, ...$ be i.i.d $\in$ $\{1, 2, ..., N\}$ and taking each value with probability $\frac{1}{N}$. Consider the range of values up to time n, $X_n=\{\xi_1,\xi_2, ..., \xi_n\}|$. Show that $X_n$ is a Markov chain. How much time is expected for $X_n$ to be absorbed at M?

Mizzle
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  • Absorbed as in reach a state where all N states are in the set? This will be a disguised form of the coupon collector problem. To see the chain is Markov you can more or less explicitly describe its transition matrix. – Ian Mar 19 '21 at 03:34
  • I find the solution here https://mat.uab.cat/matmat_antiga/PDFv2014/v2014n02.pdf. – Mizzle Mar 19 '21 at 06:29

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