A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_{0}}{2}$, when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t=t_{k}$, the variance of the random variable $n\left(t_{k}\right)$ is $\_\_\_\_\_\_\_$.
- $\frac{N_{0}}{4 R C}$
- $\frac{N_{0}}{2 R C}$
- $\frac{N_{0}}{R C}$
- $\frac{2 N_{0}}{R C}$