Polya Urn Convergence - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
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Topics: probability, convergence, urn-model, beta-distribution
Problem Description
An urn initially contains 1 red ball and 1 blue ball. A ball is drawn at random from the urn, and then it is returned to the urn along with one additional ball of the same color. This process is repeated indefinitely.
After $n$ draws, let $R_n$ be the number of red balls in the urn and $T_n$ the total number of balls in the urn. What distribution does the fraction of red balls, $R_n / T_n$, converge to as $n$ approaches infinity?
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