Consider a sample $X_1$, . . . , $X_n$ from the pdf $f_X(x; θ)$ = $\frac{|x|}{θ^2}$$I_{(−θ,θ)}$(x).
We've already found that $S=max(|X_{1:n}|,|X_{n:n}|)$ is sufficient for θ. Where $|X_{1:n}|$ denotes the absolute value of the smallest order statistic and $|X_{n:n}|$ denotes the absolute value of the largest order statistic.
The problem answering this question lies with the absolute value signs.
The question is: Show that $Q = \frac{S}{θ}$ is a pivotal quantity, and use this to provide a 95% upper confidence limit for θ.