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Using only a fair coin, how would you construct a Uniform(0,1) random variable, or an event with probability 1/3 or 1/pi?

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A random variable equals mu with probability 0.2 and is drawn from N(mu, 1) with probability 0.8. Given n samples, would you estimate mu with the sample mean or the sample median?You start with $10 and bet $1 per round on a fair coin, stopping at $20 or $0. What is the probability you reach $20?

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