Tuesday, 5 December 2006

st.statistics - Estimate population size based on repeated observation

I take the bus to work every day. Every bus has a serial number, but unlike in the German Tank Problem, I don't know if they are numbered uniformly $1...n$.



Suppose the first $k$ buses are all different, but on day $k+1$ I take one I've been on before. What is the best estimate for the total number of buses?

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