Expected value in a bivariate density

Let $(X, Y)$ be a random vector having the joint probability density function $$f(x, y)=\begin{cases} \frac{\sqrt{2}}{\sqrt{\pi}} e^{-2x} e^{-\frac{(y-x)^2}{2}}, & 0 < x < \infty, -\infty < y < \infty \ 0, & \text{otherwise.} \end{cases}$$ Then $E(Y)$ equals