Statistical Methods

Unit 2 - Probability distributions

2.8.Estimation of population size
The Hyper geometric distribution is useful in estimating the number of fish in a closed water body. Let there be N fish in the water body, N being unknown A catch of M fish is taken and marked and returned alive into the water body. After allowing a reasonable time for fish to randomly mix with unmarked fish a catch of n fish is taken. Here M and n are regarded as fixed pre-determined constants. Among these ‘n’ fish caught there will be say x marked fish, where x follows a hyper geometric distribution given as below. The maximum likelihood estimate of N is given by ;

Example 10
Five fish of a particular species which is thought to be near extinction in a certain region have been caught, tagged and released to mix into the population. After they had completely mixed with the rest of the population, a random sample of 10 of these fishes is selected. If there are 25 fish of this species in the region, what is the probability that in the second sample ;
(i) There are 2 tagged fish
(ii) At the most 2 tagged fish
Answer

Example 11
In order to estimate number of fish in a pond 200 fish were caught and tagged and released into the pond. After the tagged fish thoroughly mixed with rest of the population, a random sample of 50 fish was selected and 12 were found to be tagged. Estimate the number of fish in the pond.
Answer