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A new urn model. (English) Zbl 1093.60007
From the authors’ summary: A single urn contains $$b$$ black balls and $$w$$ white balls. For each observation, we randomly draw $$m$$ balls and note their colors, say $$k$$ black balls and $$m-k$$ white balls. We return the drawn balls to the urn with additional $$ck$$ black balls and $$c(m-k)$$ white balls. This procedure is repeated $$n$$ times and let $$X_n$$ be the fraction of black balls after the $$n$$th draw. The asymptotic properties of $$X_n$$ are investigated and it is shown that $$(X_n)$$ is a martingale which converges a.s. to a r.v. $$X$$ whose distribution is absolutely continuous.

##### MSC:
 60C05 Combinatorial probability 60G42 Martingales with discrete parameter 60F15 Strong limit theorems
##### Keywords:
martingale; symmetric polynomial; absolute continuity
Full Text:
##### References:
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