I have a simple discrete time random process that with probability $0.5$ chooses a deterministic sequence so that $X(t) = -1$, for $t<1$ and $X(t) = +1$ for $t \geq 1$, similarly with probability $0.5$ it chooses the deterministic sequence that is the negative of this, so $X(t) = +1$ for $t<1$ and $X(t) = -1$ for $t\geq 1$. Obviously the ensemble of this process is these 2 fixed sequences.
My problem is thinking about sampling this random process, say at times $t=1$, and $t=3$. If I sample $X(1)=+1$, does that mean $X(3)$ also must be $+1$, I was thinking no? Basically I'm trying to understand if this process is at all statistically different from one made of a sequence of bernoulli RV's that chose $\pm 1$ with equiprobability of $1/2$.