On a line transect survey, the observer recorded the following distances (in meters) from detected birds to the transect line: 0, 1, 1, 2, 3, 3, 4, 6, 7, 7, 9, 12, 17. The transect line is 50 m long. Estimate the density of the bird population by three of the following methods. List key assumptions that go with each method you use.
(a) Narrow strip
(b) Smooth-by-eye
(c) Exponential detectability
(d) Half-normal detectability
(e) Normal kernel
(f) Fourier series