The sizes of animal population are often estimated by using acapture-tag-recaptu

Question

The sizes of animal population are often estimated by using acapture-tag-recapture
method. In this method, k animals are captured, tagged, and thenreleased into the
population. Sometimes later, n animals are captured, and Y, thenumber of tagged animals
among the n, is noted. The probabilities associated with Y are afunction of N, the number of
animals in the population, so the observed value of Y containedinformation on this unknown
N. Suppose k=4 animals are tagged and then released. A sample ofn=3 animals is then
selected at random from the same population. Find P(?Y = 1)? as afunction of N. What value of
N will maximize P(Y= 1)? ? (i.e., find N using the MaximumLikelihood method.)

Explanation / Answer

4 animals are captured and tagged and released. So nexttime probability of recapturing a tagged animal = 4/N .

And since 3 animals are recaptured

P(Y=1) = 3c1 * (4/N)1 * (1-4/N)2

= 12(N-4)2 /N 3

Maximum value of this function is when N = 12 (remember N is aninteger and probability should be between 0 and 1)

Hope this helps and feel free to ask for any clarification

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