Logistic Process. Population X(r) is assumed to satisfy N S X(() SM (N

Logistic Process. Population X(t) is assumed to satisfy N X(t) M (N < u fixed integers). Let the birth and death rates per individual be A = - X(t)) - N) and Zsurne that individual members Of the population act independently. Ilrn, given X(t) n, rat are = an(M - n), "n On(n N). Observe that ifX(t) reaches M then the birth ratc drops to O while death rates reaches max (i.e. Over-crowding causes high death rate). Find the stationary distribution.