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Consider a white Gaussian noise process $\text{N(t)}$ with two-sided power spectral density $S_{N}\left ( f \right )=0.5\:W/Hz$ as input to a filter with impulse response $0.5e^{-t^{2}/2}$ (where $t$ is in seconds) resulting in output $Y(t)$. The power in $Y(t)$ in watts is

1. $0.11$
2. $0.22$
3. $0.33$
4. $0.44$