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You are a statistical trainee actuary working for an insurance comparison website and insurance broker. You are part of a statistical modelling team that is investigating using the serial numbers of the policies sold via the webpage to estimate the total number of policies that a certain insurance company is issuing monthly.
Assume that each policy has a serial number X taking values on the integers from 1 to N, with N being the total number of policies that the insurer of interest has issued on that month.
You observe a sample of size n, henceforth denoted by X1, . . . , Xn, which you decide to model as a sample without replacement from a discrete uniform distribution over {1, . . . , N}.
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