Evaluate the Improper Iterated Integral $\int_{0} ^ {\infty}$ $\int_{0}^{\infty} x y e^{-\left(x^{2}+y^{2}\right)} d x d y$

Multiple Choice

Evaluate the improper iterated integral
$\int_{0} ^ {\infty}$$\int_{0}^{\infty} x y e^{-\left(x^{2}+y^{2}\right) } d x d y$

A) $\frac { 3 } { 4 }$
B) $\frac { 5 } { 2 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 1 } { 4 }$
E) $\frac { 5 } { 4 }$