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Over the next 10 years, the Vera C. Rubin Observatory (Rubin) will observe ∼10 million active galactic nuclei (AGNs) with a regular and high cadence. During this time, the intensities of most of these AGNs will fluctuate stochastically. Here, we explore the prospects to quantify precisely these fluctuations with Rubin measurements of AGN light curves. To do so, we suppose that each light curve is described by a damped random walk with a given fluctuation amplitude and correlation time. Theoretical arguments and some current measurements suggest that the correlation timescale and fluctuation amplitude for each AGN may be correlated with other observables. We use an expected-information analysis to calculate the precision with which these parameters will be inferred from the measured light curves. We find that the measurements will be so precise as to allow the AGNs to be separated into up to ∼10 different correlation-timescale bins. We then show that if the correlation time varies as some power of the luminosity, the normalization and power-law index of that relation will be determined to$\mathit{}({10}^{-4}\%)$. These results suggest that with Rubin, precisely measured variability parameters will take their place alongside spectroscopy in the detailed characterization of individual AGNs and in the study of AGN population statistics. Analogous analyses will be enabled by other time-domain projects, such as CMB-S4.