Question: Find the extinction probability for a GaltonWatson process with offspring distribution in the cases (a) .k/ D 0 for all k > 2, (b) .k/

Find the extinction probability for a Galton–Watson process with offspring distribution in the cases

(a) .k/ D 0 for all k > 2,

(b) .k/ D bak1 for all k 1 and a; b 2 0; 1OE with b 1

a. (According to empirical studies by Lotka in the 1930s, for a D 0:5893 and b D 0:2126 this describes the distribution of the number of sons of American men quite well, whereas, according to Keyfitz [33], the parameters a D 0:5533 and b D 0:3666 work best for the number of daughters of Japanese women.)

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