Each individual in a biological population is assumed to give birth at an exponential rate A and to die at an exponential rate . In addition, there is an exponential rate of increase due to immigration. However, immigration is not allowed when the population size is N or larger

(a) Set this up as a birth and death model.

(b) If N = 3, 1 == A, = 2, determine the proportion of time that immigration is restricted.