Background: With aggressive scaling of single-expose (SE) extreme ultraviolet (EUV) lithography to the sub-7-nm node, stochastic variations play a prominent role in defining the lithographic process window (PW). Fluctuations in photon shot noise, absorption, and subsequent chemical reactions can lead to stochastic failure, directly impacting electrical yield. Aim: Fundamental characterization of the mode and magnitude of these variations is required to define the threshold for failure. Approach: A complementary series of techniques is enlisted to probe the nature and modulation of stochastic variation in SE EUV patterning. Unbiased line edge roughness (LER), local critical dimension uniformity (LCDU), and defect inspection techniques are employed to monitor the frequency of stochastic variations leading to failures in line/space (L/S) and via patterning. Results: When characterizing different resists and illumination conditions, there is no change in unbiased LER or via LCDU with increasing critical dimension (CD). Stochastic defect density is correlated with CD for both L/S and via arrays, and there is a strong correlation with L/S electrical yield data. Conclusions: Traditional 3σ LER and via LCDU measurements are not sensitive enough to define and improve PW. For PW centering and yield improvement, stochastic defect inspection is a necessity.