Suppose that $Y$ is a r.v. such that $Y\sim N(\mu_Y,\sigma_Y^2)$ and $X=\frac{|Y|}{2}$. Then the expectation of the r.v. $X$ is the following:
$$E(X)=E\left(\frac{|Y|}{2}\right)=\dfrac{1}{2}E(Y^{+}+Y^{-})$$, where $Y^{+}=\max\{0,Y\}$ and $Y^{-}=\max\{0,-Y\}$. Given that, the pdf and the cdf of the Gaussian normal distribution are known, what is the expectation of the r.v. $X$?