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3. We want to estimate the number of fish, say N, in a pond. We proceed as follows. We catch r fish and mark them. We then set them free. After some time, we catch n fish (without putting them back). Of these, X are marked. Consider r and n as constants we choose ourselves, and let X be the observation. (i) Formulate a suitable statistical model. (ii) Give an intuitively reasonable "estimate" of N based on the observation. (iii) Answer the previous questions if, the second time we catch fish, they are put back directly after catching them (sampling with replacement).

          3. We want to estimate the number of fish, say N, in a pond. We proceed as follows. We catch r fish and mark them. We then set them free. After some time, we catch n fish (without putting them back). Of these, X are marked. Consider r and n as constants we choose ourselves, and let X be the observation.
(i) Formulate a suitable statistical model.
(ii) Give an intuitively reasonable "estimate" of N based on the observation.
(iii) Answer the previous questions if, the second time we catch fish, they are put back directly after catching them (sampling with replacement).

3. We want to estimate the number of fish, say N, in a pond. We proceed as follows. We catch r fish and mark them. We then set them free. After some time, we catch n fish (without putting them back). Of these, X are marked. Consider r and n as constants we choose ourselves, and let X be the observation.
(i) Formulate a suitable statistical model.
(ii) Give an intuitively reasonable "estimate" of N based on the observation.
(iii) Answer the previous questions if, the second time we catch fish, they are put back directly after catching them (sampling with replacement).

Added by Milagros P.

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