The random variable we are going to study is
X the number of
white balls selected:
This only takes on positive values for:
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
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.