Final answer:
Probabilistic estimating takes into account uncertainty by using statistical methods to predict a range of outcomes, while deterministic estimating provides a single, fixed outcome. Mathematical models help in both approaches to estimate and normalize costs, but probabilistic models are usually more comprehensive for risk management.
Step-by-step explanation:
When analyzing whether probabilistic estimating is better than deterministic for scheduling tasks and resource cost, it is important to understand the difference between the two methods. Probabilistic estimating, also known as stochastic estimating, involves using statistical methods to predict outcomes by accounting for variability and uncertainty. This is often done through generating a range of possible outcomes and their probabilities. Deterministic estimating, on the other hand, relies on fixed inputs and provides a single, definitive outcome without accounting for uncertainty.
Mathematical models are critical in both approaches. They help in estimating costs and analyzing the science behind a technique as well as the costs associated with materials, fabrication, operation, and maintenance. These costs are normalized to facilitate comparison. For instance, to compare various water treatment methods, costs could be normalized to cost per thousand gallons of water treated.
While deterministic models are simpler and more straightforward to use, probabilistic models provide a more comprehensive picture by considering the range of possible scenarios and their likelihoods. This can lead to better risk management and planning in projects where uncertainty is a significant factor.