I have a following problem:
Imagine you have a hat with many different balls in it and you want to estimate, how many balls are totally in the hat. The only think you are allowed to do is to take one ball at the time, write down its ID and put it back.
I would like to obtain a reasonable guess of the total count of balls in finite time (of course, the longer I do my observation, the more accurate result I get). Or better, how my guess evolves in time with my observation.
I'm pretty sure the problem has been already solved, I just couldn't found anything similar on the internet.
Motivation: for example you hear to a radio station and you want to guess, how many songs they have in total.
Thank you very much for helping :)