Formula_21543

\[\begin{gathered}\xi_{0}=1, \quad \mathrm{P}\left\{\xi_{1}=k\right\}=p_{k}, \quad \sum_{k=0}^{\infty} p_{k}=1, \\P_{j k}=\mathrm{P}\left\{\xi_{n+1}=k \mid \xi_{n}=j\right\}=\sum_{i_{1}+i_{2}+\ldots+i_{j}=k} p_{i_{1}} p_{i_{2}} \ldots p_{i_{j}} .\end{gathered}\]