Let $(Y\_n)\_{n\in\mathbb{N}\_0}$ be a sequence of random variables with an arbitrary distribution $q$ and existing expectancy value.

How can I check, if the following sequences hold the markov property or the martingale property?

1) $(S\_n)\_{n\in\mathbb{N}\_0}$, where $S\_n:=Y\_1+...+Y\_n$

2) $(T\_n)\_{n\in\mathbb{N}\_0}$, where $T\_n:=Y\_{n-1}+Y\_n$

3) $(M\_n)\_{n\in\mathbb{N}\_0}$, where $M\_n:=max\{Y\_1,...,Y\_n\}$

Does a sequence exist, which hold the martingale property, but not the markov property?

I really hope someone can help with these questions.

Greetings