Is there a strategy for combining the German tank and secretary problem?

[Gerenuk]

Is it possible to give a strategy for the combined problem of
http://en.wikipedia.org/wiki/German_tank_problem
and
http://en.wikipedia.org/wiki/Secretary_problem

So I'm observing tanks with serial numbers and I'm allowed only the keep the last one. I also don't know how many there are in total. My task is to (increase change of getting the highest number) or (achieve the highest average serial number on the tank I'm keeping). The distribution of serial numbers is uniform. Another case would be if it's normal.

Basically it is the secretary problem with an unknown number of applicants, but moreover this unknown number if applicants has to be estimated given the observed incoming samples. The assumed distribution of all samples could be uniform or maybe also normal.

Has anyone heard of an article where this problem is considered? Or how do I find such an article?

 

[bpet]

Basically it is the secretary problem with an unknown number of applicants

Interesting problem. Have you tried the survey article that was listed in the wikipedia article references? It's from 1983 but might say if the same problem is solved under a different name.

Also, how could serial numbers be drawn from the normal distribution?

 

[Gerenuk]

Also, how could serial numbers be drawn from the normal distribution?

Actually I meant this as two different cases. Serial numbers from a uniform distribution. And on the other hand some other cardinal value from a normal distribution like the height of people (with apriori unknown mean height).

I just downloaded the survey article. Hope I find some time to go through it soon.