extinct al U1 Exercise 9.12 Let μ a of Theorem et μ and σ 2 be...

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extinct al U1 Exercise 9.12 Let μ a of Theorem et μ and σ 2 be the mean and vari 98 to show that the variance of Zn, ance of the family-size distribution. Adapt the proof the size of the nth generation of the branching process, is given by 2 nơ if, 1, Theorem 9.8 The mean value of Zn is (9.9) where u - kp is the mean of the family-size distribution Proof By the theory of probability generating functions, E(Zn) G,(1) by (4.26) -G-GI))G(I) = Gn-1 (1)G,( 1 ) by (9.5) since G (1) = 1, by (4.9) Therefore