Solution
= Solution
If $\lambda P=\lambda$, <induction> gives $\lambda P^n=\lambda$ for all $n\ge0$. By (c), the marginal distribution at time $n$ is consequently $\boxed{\lambda}$. Such a probability vector is a <stationary distribution>.
= Solution
If $\lambda P=\lambda$, <induction> gives $\lambda P^n=\lambda$ for all $n\ge0$. By (c), the marginal distribution at time $n$ is consequently $\boxed{\lambda}$. Such a probability vector is a <stationary distribution>.