Dear

I am stuck with this question. Please help me out how to solve this problem.

Thanks in advance.

Let $\displaystyle \xi = \left( {{\xi _0}, \cdots ,{\xi _n}} \right)$ be Markov Chain with variable X and $\displaystyle f = f(x)\,(x \in X)$ a function. Will the sequence $\displaystyle \left( {f({\xi _0}), \cdots ,f({\xi _n})} \right)$ form a Markov Chain? Will the reversed sequence?