Define 'stochastic modeling' in the context of engineering.

Stochastic modeling refers to approaches that incorporate randomness and uncertainty into the analysis and modeling of systems within engineering. In such models, various random variables are used to capture the inherent unpredictability of real-world processes. This is essential in fields like engineering because many systems are influenced by uncontrollable factors, leading to variations in outcomes.

By using stochastic models, engineers can simulate different scenarios, weigh risks, and make predictions that account for these uncertainties. This is particularly useful in fields such as reliability engineering, financial engineering, and operations research, where understanding the range of possible outcomes is crucial for making informed decisions.

Deterministic models, in contrast, operate under the assumption that given a set of inputs, outcomes will always be the same, which does not accurately reflect many real-world situations where variability is present. Stochastic modeling thus provides a more comprehensive understanding of complex systems where the elements of chance play a significant role.