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At time t0 = 0, a fair coin is tossed and lands heads. Then, at a random time T > 0, the coin is tossed

At time t0 = 0, a fair coin is tossed and lands heads. Then, at a random time T > 0, the coin is tossed again. Given a t > 0, compute the probability that the coin shows heads at time t, if T is the moment of the first event in a Poisson process with parameter . How will the answer change if the coin is not fair?

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