Solution
= Solution
The second moment of the <mixed probability distribution> is $\mathbb E[Y^2]=\tfrac12(-1)^2+\tfrac12\int_0^\infty y^2e^{-y}dy=1/2+1=3/2$. Since the mean is zero,
$$
\boxed{\operatorname{Var}(Y)=\frac32.}
$$
= Solution
The second moment of the <mixed probability distribution> is $\mathbb E[Y^2]=\tfrac12(-1)^2+\tfrac12\int_0^\infty y^2e^{-y}dy=1/2+1=3/2$. Since the mean is zero,
$$
\boxed{\operatorname{Var}(Y)=\frac32.}
$$