(Requires mathematical statistics.) Maximum likelihood estimation of N in large samples. Suppose that n1 of the N...
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Suppose that n1 of the N fish in a lake are marked. An SRS of n2 fish is then taken, and m of those fish are found to be marked. Assume that N, n1, and n2 are all €œlarge.€ Then the probability that m of the fish in the sample are marked is approximately:
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a. Show that Ṅ= n1n2 / m is the maximum likelihood estimator of N.
b. Using maximum likelihood theory, show that the asymptotic variance of Ṅ is approximately N2 (N ˆ’ n1) / (n1n2).
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Step by Step Answer:
a Setting the derivative equal to zero we have m n1 n 2 mn 1 ...View the full answer
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