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5965概率困难数值题long

Branching Process Extinction Probability

题目

A Galton-Watson branching process starts with one individual. Each individual independently has 0 offspring with probability 1/4, 1 offspring with probability 1/4, and 2 offspring with probability 1/2. Let q be the extinction probability. Using that q^{Z_n} is a martingale (where Z_n is the generation-n population), find q.

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