Understanding Mixed Probability Expressions in Engineering Courses
DOI:
https://doi.org/10.54097/g19mtz71Keywords:
Mixed Joint Probability, Mixed Conditional Probability, Product RuleAbstract
The gap between basic and specialized probability knowledge for engineering students is addressed by extending core concepts. In the basic course, students typically encounter probability expressions involving either random events or continuous random variables, but not both simultaneously. However, specialized courses in fields such as communication systems and machine learning require handling both types together. The meanings and properties of mixed joint and conditional probability (density) are given, and the product rule is extended to cover these cases. Introducing these topics can help students to transition smoothly and prepares them for more complex applications.
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[1] Athanasios Papoulis and S. Unnikrishna Pillai (2002). Probability, random variables, and stochastic processes (fourth edition). McGraw-Hill.
[2] John A. Gubner (2006). Probability and random processes for electrical and computer engineers. Cambridge University Press.
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[4] Christopher M. Bishop (2006). Pattern recognition and machine learning. Springer.
[5] Carl Edward Rasmussen and Christopher K. I. Williams (2006). Gaussian processes for machine learning. MIT Press.
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