After $t$ tosses of a fair coin, let $H(t)$ be the number of heads observed so far; $T(t)$ be the number of tails observed so far; $X(t)=H(t)-T(t)$. Which one of $H(t)$, $T(t)$ and $X(t)$ are
a) AR(1). My thoughts: none of $H(t)$, $T(t)$ and $X(t)$ are AR(1) since they cannot be written as functions of previous time
b) Martingale. Thoughts: $H(t)$ & $T(t)$ are not, $X(t)$ is
c) Markov process
d) For what integer values of $n>1$ is $X(t)^n$ a martingale?
Can anyone check if I'm on the right track? Thanks!