Solution
= Solution
Here $F_1(s)=1/(2-s)$ and $\mu=1$, so extinction is certain. Iteration gives
$$
F_n(s)=\frac{n-(n-1)s}{n+1-ns},
$$
and $\mathbb P(X_n=0)=F_n(0)=n/(n+1)$.
= Solution
Here $F_1(s)=1/(2-s)$ and $\mu=1$, so extinction is certain. Iteration gives
$$
F_n(s)=\frac{n-(n-1)s}{n+1-ns},
$$
and $\mathbb P(X_n=0)=F_n(0)=n/(n+1)$.