5.41 On each of T separate visits to N sites it is recorded whether or not a particular bird species is present or absent. An illustration of the data that may result from such a study is given below, for the American blue jay, Cyanocitta cristata. Here T = 11 and N = 50.

Number of detections Species 0 1 2 3 4 5 6 7 8 9 10 11 Jay 17 9 11 6 5 2 0 0 0 0 0 0 For any site, let Y denote the number of visits on which a jay was detected.

A particular model for detection gives the following expressions for the probability distribution of Y :