Can you please answer this asap for an assignment Discuss th

Discuss the main difference between direct and inverse sampling for a. estimating the population size N. b. We want to estimate the total number of eagles in a wildlife preserve. A random sample of 200 eagles is trapped, tagged, and then released. In the same month, a second sample is drawn until 35 tagged eagles are recaptured. The sample size needed to get 35 tagged eagles is 100 i) Estimate N, the total size of the population, and place a bound on the error of estimation.

Solution

Mark and recapture is a method used in ecology to estimate an animal population\'s size. A portion of the population is trapped, tagged, and released. Later, another portion is trapped and the number of tagged individuals within the sample is counted. Since the number of tagged individuals within the second sample should be proportional to the number of tagged individuals in the whole population, the total population size can be estimated by dividing the number of tagged individuals by the number of tagged individuals in the second sample.

(i) The Lincoln–Petersen method, also known as Lincoln index can be used to estimate population size if only two visits are made to the study area. The formula is

N = Kn/k where,

N = Number of animals in the population

n = Number of animals marked on the first visit

K = Number of animals captured on the second visit

k = Number of recaptured animals that were marked

In the given problem, N is to be found out.

n = 200, K = 100, k = 35

Therefore, N = 100 x 200/35 = 571.42 which can be truncated to 571.

(ii) The Lincoln–Peterson estimator is unbiased as sample size approaches infinity, but is biased when small sample sizes are used.