Question 1 The offspring distribution in a GaltonWatson bran

Question #1 The offspring distribution in a Galton-Watson branching process is binomial with mean E[Y] = 1.2, and variance 0.96. (i) The Newton-Raphson method is used to solve x = pi Y(x) where pi Y(s) is the probability generating function for random variable Y. Show that the iterating formula is given by Xn+1=0.8-xn/(0.8+0.2xn)^-5 - 1.2 (ii) Hence solve for the probability of ultimate extinction of the branching process, giving your answer to 4 decimal places.

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