Solution
= Solution
Since the <probability density function> is an <even function>, $xf(x)$ is an <odd function>. Its <integral> over the symmetric support vanishes, so
$$
\boxed{\mathbb E[X]=0.}
$$
= Solution
Since the <probability density function> is an <even function>, $xf(x)$ is an <odd function>. Its <integral> over the symmetric support vanishes, so
$$
\boxed{\mathbb E[X]=0.}
$$