Probability Theory for Scientists and Engineers

In this case study I attempt to untangle this pedagogical knot to illuminate the basic concepts and manipulations of probability theory and how they can be implemented in practice. Our ultimate goal is to demystify what we can calculate in probability theory and how we can perform those calculations in practice. We begin with an introduction to abstract set theory, continue to probability theory, and then move onto practical implementations without any interpretational distraction. We will spend time more thoroughly reviewing sampling-based calculation methods before finally considering the classic applications of probability theory and the interpretations of the theory that then arise.

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