I have wrestled with this problem before, and I *think* that the problem is not well-formed as stated. There needs to be a prior distribution, a given probability that n takes on different values. I started collecting Nantucket Nectars Iced Tea caps at some point, and when I got my first duplication I spent some hours trying to figure out what I now knew about the total number of unique caps. As I recall, it turned out that the answer was "nothing except that it's at least 17". On Wed, Feb 3, 2016 at 12:13 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Mama don't allow no p*l*t*c*l probability here: so I've gone back to collecting --- computationally rather expensive --- coupons. [ A man should have an occupation of some sort. ]
I don't know in advance how many distinct coupons are available, but have collected m among which there are just k distinct. What is the probability that n distinct coupons are available? What is the most likely value of n ? What are asymptotic expressions for large m ?
Fred Lunnon
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun