105.The Cloning Robot
★★★markov chainsJane Street
Each morning every robot independently does one of four things with equal probability: destroys itself, does nothing, clones itself once (becoming 2 robots), or clones itself twice (becoming 3 robots). Starting from a single robot, what is the probability that the population eventually dies out completely?
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This is a branching process. The extinction probability is the smallest non-negative fixed point of the offspring generating function.
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