(Requires mathematical statistics ) Maximum likelihood estimation of N in large samples 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 large Then the probability that m of the fish in the sample are marked is approximately a Show that aacute sup1 n1n2 m is the maximum likelihood estimator of N b Using maximum likelihood theory, show that the asymptotic variance of aacute sup1 is approximately N2 (N n1) (n1n2) n12 n (N) (m ) (N

Question: (Requires mathematical statistics.) Maximum likelihood estimation of N in large samples. Suppose that n1 of the N fish in a lake are marked. An SRS

(Requires mathematical statistics.) Maximum likelihood estimation of N in large samples.
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:

a. Show that á¹„= n1n2 / m is the maximum likelihood estimator of N.
b. Using maximum likelihood theory, show that the asymptotic variance of á¹„ is approximately N2 (N ˆ’ n1) / (n1n2).

n12-n (N) = (m ) (N

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