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Unformatted text preview: 5 175 176 176 176 177 179 vi CONTENTS Preface A key objective of these notes is to convey how to deal with uncertainty in both qualitative and quantitative ways. Uncertainty is typically modeled as randomness. We must make decisions with partial information all the time in our daily lives, for instance when we decide what activities to pursue. Engineers deal with uncertainty in their work as well, often with precision and analysis. A challenge in applying reasoning to real world situations is to capture the main issues in a mathematical model. The notation that we use to frame a problem can be critical to understanding or solving the problem. There are often events, or variables, that need to be given names. Probability theory is widely used to model systems in engineering and scientific applications. These notes adopt the most widely used framework of probability, namely the one based on Kolmogorov’s axioms of probability. The idea is to assume a mathematically solid definition of the model. This structur...
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