(20 points) Let X\" be a branching process with Kg 2 10 and descen dent generation distribution distributed like 3;" where Pt=0)=%=P(=1)=%aandP(=2}=%- Specically, X13210 X11. n+1 Xn+1 : Z at; } k=1 where 5;\") are i.i.d. random variables distributed like 5. {a} Find the probability that the population eventuallyr goes extinct. Show all of your work and explain each step. Hint: Notice that the pmbtem says that XI] = 10. {b} For each a E {1, 2, 3, 4, ...} calculate EX\". Show all of your work and explain each step. Hint: Notice that the pmbtem says that XI] = 10