A simulation-based study of Kramers escape problem in the bistable well of a ferroelectric capacitor is presented. This problem deals with the escape of a particle undergoing Brownian motion over an energy barrier. Using this framework under the assumption of homogeneous polarisation switching according to the Landau-Ginzburg-Devonshire (LGD) theory, two prospective device applications based on a ferroelectric capacitor are also outlined, namely true random number generation (TRNG) and stochastic resonance (SR). Our simulation results for the former demonstrate that by adding white noise and an appropriately tuned voltage pulse to the material system, it is possible to facilitate controlled, probabilistic switching between its two stable polarisation states. We predict that this could provide the theoretical framework for practical implementations of TRNGs. In addition, we also develop a theory for stochastic resonance in a ferroelectric using linear response theory. We show, analytically and via numerical simulations that the addition of an optimal amount of noise to a weak periodic signal given as an input to a non-linear system can enhance its detection.