Suppose a pond has N fish where N is unknown and we want to estimate it. We first capture n fish, tag each one, and rele

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Suppose a pond has N fish where N is unknown and we want to estimate it. We first capture n fish, tag each one, and rele

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Suppose A Pond Has N Fish Where N Is Unknown And We Want To Estimate It We First Capture N Fish Tag Each One And Rele 1
Suppose A Pond Has N Fish Where N Is Unknown And We Want To Estimate It We First Capture N Fish Tag Each One And Rele 1 (44.65 KiB) Viewed 102 times
Suppose a pond has N fish where N is unknown and we want to estimate it. We first capture n fish, tag each one, and release them back to the pond. We then capture m fish, and count the tagged ones to be X. Assume n and m are known and both captures are random. (i) What is the underlying distribution of X? Show your work (ii) Suppose we observe X = r. Find the MLE of N. Hint: this is a discrete distribution, and taking derivative is not feasible. It would be easier if you think about if N = no is the MLE, how would P(X|N) change around no.
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