Consider a species of animal which only breeds during the spring. Assume that every female produces (on the average) 6 female offspring which survive to breed in the next year. Also, suppose that of the adults in a particular breeding season, only 1/4th will survive to the next spring. Each year, we model this fraction by a continuous random variable which is uniform on (0, 1). Let Nm be the female population after m years and assume No = 80. (a) Formulate a modeling equation. This equation should have a random variable in it. Be sure to specify what type of random variable it is. (b) Use your equation in part (a) to find E[Nā] and V(Nā). (c) Use software to make a graph with 10 runs of the model over 20 years each.
