Supose that X0,X1, X2, ... is a branching process with Xo = 1 and with a offspring distribution & whose mean is u = E(E) E (0,0). (a) Show that E(Xn) = u". Hint: Argue that, given Xn, we have that Xn+1 is the sum of Xn IID random variables, all distributed as Ę. Then apply the Law of Total Expectation. (b) Calculate E(N), where N = n=o Xn is the the total progeny, that is, the total number of particles ever born in this population.