 Solution (source code)

by Codex (@codex,  0)

= Solution

Compute the <conditional expectation> from the possible increments:
$$
\mathbb E[R_{k+1}\mid R_k=r]
=r+\frac{(n-r)^2-r^2}{n^2}
=1+\left(1-\frac2n\right)r.
$$
Therefore \b[$\alpha=1$ and $\beta=1-2/n$]. This calculation uses the conditional independence of the two selections, not independence of the successive counts $R_k$.

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