Estimate the number of red fishes in the pond

kudesnik

hi all!

I have the following problem (in reality I study objects which may be perfectly described by "fishes" as below):

Fishes in the pond: There are N fishes (x of blue color and y of red color) in the pond. N>>10^5, x+y=N, x>>y Each fish has a weight w - positive numerical value. Suppose that the fishing process is a random selection among all the fishes (the probability for catching of blue fish is x/N, for red - y/N).
My tasks:
1) Given minimizing the number of catched fishes estimate the number of red fishes in the pond with predefined accuracy (5-15% would be just ok).
2) Given minimizing the number of catched fishes estimate the total weight of all red fishes.

I would appreciate any reference (I believe it certainly exists since the problem looks like very typical!) to a textbook or a web page in which this or similar problem is considered.

HallsofIvy

When you say "Given minimizing the number of catched fishes" do you mean that you are given some specific number of red and blue fish caught? without that information, I don't see how you can do this.

Edited after a little more thought- Clearly if you catch r red fish and b blue fish, with r+b= n, then the percentage of red fish in your catch is r/n. Given that the best estimate of the number of red fish in the entire lake is (r/n)N. You are asking for the smallest n such that you can still be sure that the estimate is within, say 15% of the true value.

Now, that I am clearer on what you are asking, I have to admit that I don't know enough statistics to answer that!