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Estimate the number of red fishes in the pond

  1. Oct 17, 2005 #1
    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.
     
  2. jcsd
  3. Oct 22, 2005 #2

    HallsofIvy

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    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!
     
    Last edited: Oct 22, 2005
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