Answer Happy

= = = - = = 1. Consider a discrete-time single-type branching process Xn with a Poisson progeny distribution and the corresponding generating function Q(s) = E (sX1) = e^(s–1). . (a) Write a function to simulate Xn starting from Xo = 1. (b) Estimate qn = Pr(Xn = 0) for n = 5, 15, 30 and l = 1.4 by simulating the branching process N = 1000 times. (c) Compare your simulation-based estimate with a numerical solution that uses the Newton's method to solve equation Q(s) (Recall that Newton's method for solving an algebraic equation f(x) = 0 pre- scribes a recursion Xn+1 = In - f(xn)/f'(xn).) = = S.