Solution
= Solution
Include the negative atom as well as the continuous part in the <expected value>:
$$
\boxed{\mathbb E[Y]=\frac12(-1)+\frac12\int_0^\infty ye^{-y}dy=-\frac12+\frac12=0.}
$$
= Solution
Include the negative atom as well as the continuous part in the <expected value>:
$$
\boxed{\mathbb E[Y]=\frac12(-1)+\frac12\int_0^\infty ye^{-y}dy=-\frac12+\frac12=0.}
$$