Understanding Mixed Probability Expressions in Engineering Courses

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.