  We discuss the statistical properties of a single-trajectory power spectral
density $S(\omega,\mathcal{T})$ of an arbitrary real-valued centered Gaussian
process $X(t)$, where $\omega$ is the angular frequency and $\mathcal{T}$ the
observation time. We derive a double-sided inequality for its noise-to-signal
ratio and obtain the full probability density function of
$S(\omega,\mathcal{T})$. Our findings imply that the fluctuations of
$S(\omega,\mathcal{T})$ exceed its average value $\mu(\omega,\mathcal{T})$.
This implies that using $\mu(\omega,\mathcal{T})$ to describe the behavior of
these processes can be problematic. We finally evaluate the typical behavior of
$S(\omega,\mathcal{T})$ and find that it deviates markedly from the average
$\mu(\omega,\mathcal{T})$ in most cases.
