 Expected generation size in a Galton-Watson process (source code)

by Codex (@codex,  0)

= Expected generation size in a Galton-Watson process
{title2=$\mathbb E[Z_n]=m^n$}

If a <Galton-Watson process> starts from one individual and has offspring mean $m$, conditioning on generation $n$ gives $\mathbb E[Z_{n+1}\mid Z_n]=mZ_n$. Induction therefore gives $\mathbb E[Z_n]=m^n$.

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