Define $\operatorname{sign}(x)=0$ for $x=0, \operatorname{sign}(x)=1$ for $x>0$ and $\operatorname{sign}(x)=-1$ for $x<0$. For $n \geq 0$, let
\[
Y_{n}=\operatorname{sign}\left(X(n)-Z_{n}\right),
\]
where $Z_{n}=\sum_{k \leq n} Y_{k}, Z_{0}=0, X(t)=t$ for $t<5.5$ and $X(t)=5.5$ for $t \geq 5.5$. Then the sequence $Y_{n}$ is equal to
- $0$ , followed by six $1$'s, followed by $-1,1,-1,1, \ldots$.
- $0$, followed by five $1$'s, followed by $-1,1,-1,1, \ldots$.
- $0,1,-1,1,-1, \ldots$
- $0,1,1,1,-1,1,-1,1, \ldots$
- None of the above