) Let Xn be a branching process with X₀ = 10 and descendent generation distribution distributed like ? where :

P($ = 0) = = P(6 = 1)= = and P(: = 3)= Specifically, Xo = 10 where girl "are Lid. random variables distributed like {. (a) Find the probability that the population eventually goes extinct. Show all of your work and explain each step. Hint: Notice that the problem says that No = 10. (b) For each n e {1, 2,3, 4,...} calculate EXn