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## Hypergeometric Random Variable 11/3

A sample of size n is chosen at random from an urn containing N balls of which m are white. This is called a draw without replacement.

The random variable we are going to study is X the number of white balls selected: This only takes on positive values for: Example:
Tagging animals, N unknown, we conduct a tagging experiment by catching and marking m animals and recapture i of them that are tagged, out of the recapture sample of size n. We find it by maximising the probability of P(X=i)=Pi(N).

To see which N maximises this we notice that : This ratio is greater than 1 if and only if This increases and then decreases and is max at floor(mn/i). This is what is called the maximum likelihood estimate of N.

Example: There are 50 tagged deer in the forest, mark them and release them, a subsequent catch n=40, of which 4 are found to have marks then .

Remark: If we supposed that probability of finding tagged animal is binomial, we get the same conclusion.    Next: Geometric 11/3 Up: Special Distributions Previous: Odds Ratios and Mode
Susan Holmes
1998-12-07