A real band-limited random process $X(t)$ has two-sided power spectral density
$$S_{X}(f)= \begin{cases} 10^{-6} (3000-\mid f \mid) \text{Watts/Hz} & \text{for } \mid f \mid \leq 3 kHz \\ 0 & \text{otherwise} \end{cases}$$
where $f$ is the frequency expressed in Hz.The signal $X(t)$ modulates a carrier $\cos16000\pi t$ and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of $8$ $kHz$ and band-width of $2$ kHz. The output power (in Watts) is ___________.