Answer Happy

a 2. Suppose we are interested in estimating the mean of the progeny distribution u of a discrete-time single-type branching process. = = (a) One way of going about this task is to equate the number of particles present at time n, Xn, with the corresponding expectation E(Xn | Xo = 1). Show that - the resulting estimate ð underestimates ui on average. In other words, prove that E(ū) u. (b) Another method of moments uses equation E(Xn) E(Xn-1)u to arrive at an estimate if Xn-1 > 0 û = (1) 1 if Xn-1 = 0. Show that Elû) = uPr(Xn-1 > 0) + Pr(Xn-1 = 0). (c) Calculate ECâ) for the Poisson progeny distribution in the problem 1(a) using X= 1.1 and n = 20. Xn Xn-1 = = = - =