Consider a branching process Xn,nge0. Let X0=1 and assume that E(sumn=0^infty Xn)<infty. Then, the extinction probability:

Q179Section III (Statistics)179 of 190

A finite expected total progeny forces $m<1$ and certain extinction

Consider a branching process $\{X_n,n\ge0\}$ . Let $X_0=1$ and assume that $E\bigl(\sum_{n=0}^\infty X_n\bigr)<\infty$ . Then, the extinction probability:

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