 Statistical Model Checking, SMC, is a type of algorithm used to verify specifications of interest on an ensemble of cyber-physical systems. It uses sequential algorithms to draw enough samples from the system to determine if it meets the specified requirements. However, these algorithms can leak information about the samples, potentially compromising the privacy of users. To address this issue, we propose a new form of differential privacy called Expected Differential Privacy, EDP, which relaxes the conservative requirement of bounding the sensitivity of the output of the algorithm to any perturbation for any dataset. We then propose a novel exponential mechanism that randomizes the termination time of the algorithm to achieve EDP. Finally, we demonstrate the utility of our proposed algorithm through a case study. This article was authored by Yu Wang, Husein Sibai, Mark Yan, and others.