= Solution
A <branching process> models reproduction through successive generations. In the <Galton-Watson process> used here, every individual independently produces a nonnegative integer number of offspring with a common <offspring distribution>; these reproduction counts are independent across individuals and generations. If $X_n$ is the generation size, then
$$
X_{n+1}=\sum_{j=1}^{X_n}\xi_{n,j},
$$
where the $\xi_{n,j}$ have that distribution and the empty sum is zero. Thus \b[zero is absorbing]: once a generation is empty, every subsequent generation is empty.
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