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Imagine I have some hypothetical particle that decays over time, where $\mu$ is the mean decay time, and where the probability of each decay event is governed by some unknown probability distribution. If I really need to specify a probability distribution, let's say it's gaussian, and has a fat tail in one direction or the other.

I'd like to make a clock with this particle, albeit a primitive one, which works by simply counting the number of decay events over time and multiplying by $\mu$. If I start my clock at time $t_0$ (measured with a wall clock), and I wait an interval of time $T$ (again, measured with the wall clock), how accurately will my particle clock match up as a function of $\mu$?

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