How to find the expected value of x with pdf $f(x)=\frac{1}{2\sigma}\exp\left(-\frac{|x|}{\sigma}\right)$, where x takes all real numbers.
The original question asks to find the Method of Moment estimator of $\sigma$, so I was thinking to find the expected value of $x$ first, and rearrange it to get the estimator of $\sigma$.
I tried to integrate $\int xf(x) \, dx$ from $-\infty$ to $0$ and from $0$ to $\infty$, and I got $\sigma$ for $0$ to $\infty$, but I couldn't solve $-\infty$ to $0$.