  Many statistical properties of the aperiodic variability observed in X-ray
radiation from accreting compact objects can be naturally explained by the
propagating fluctuations model. This considers variations in mass accretion
rate to be stirred up throughout the accretion flow. Variations from the outer
regions of the accretion flow will propagate towards the central object,
modulating the variations from the inner regions and eventually modulating the
radiation, giving rise to the observed linear RMS-flux relation and also
Fourier frequency dependent time lags. Previous treatments of this model have
relied on computationally intensive Monte Carlo simulations which can only
yield an estimate of statistical properties such as the power spectrum. Here,
we find exact and analytic expressions for the power spectrum and lag spectrum
predicted by the same model. We use our calculation to fit the model of Ingram
& Done (2012) to a power spectrum of XTE J1550-564. The result we present here
will apply to any treatment of the propagating fluctuations model and thus
provides a very powerful tool for future theoretical modelling.
