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California issues license plates in numeric order (if we turn the letters into numbers). I have fun noticing the latest plate I have seen. I am interested in what you can derive from a series of these observations. I understand that sampling from $\{1,2,3...n\}$ the only useful data is the highest value you have seen.

Let's oversimplify the problem. Assume the highest plate issued is $N_0+n*t$, $n$ in plates/day and $t$ in days. Assume a similar number of low valued plates come off the road each day. I don't observe a consistent number of plates each day, but it averages out. Over a long time, the increase in highest plate seen should give a measure of $n$. The only other data I have is how frequently I see a new highest plate. Does that give some measure of how far my highest plate is from the highest issued?

As we are asked to cite the source of a question, I made it up. You probably guessed.

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Are you familiar with the German Tank Problem? – whuber Oct 13 '10 at 3:01
No, I wasn't. Thanks – Ross Millikan Oct 13 '10 at 4:43
An [original], [original-problem], [homegrown] or other such tag would be nice for these things. – T.. Oct 14 '10 at 11:28
up vote 3 down vote accepted

Joseph Gallian has decrypted many of the US state license plate and driver's license codes.

I think he used Markov chain models. As whuber mentioned your problem is similar to the German tanks for which the subject reference is "extreme value statistics".

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