Convolutions and Adding Random Variables, Visually Explained

Explore the visual explanation of convolutions and adding random variables in this 27-minute video. Dive into the connections to the central limit theorem through engaging animations and clear explanations. Begin with an introductory quiz before delving into discrete cases using diagonal slices and flip-and-slide techniques. Learn the discrete formula and transition to continuous cases, examining examples with uniform distributions. Gain insights into the central limit theorem and revisit the intro quiz to solidify understanding. Benefit from custom animations created using the manim Python library, enhancing the learning experience of complex mathematical concepts.

- Intro quiz
- Discrete case, diagonal slices
- Discrete case, flip-and-slide
- The discrete formula
- Continuous case, flip-and-slide
- Example with uniform distributions
- Central limit theorem
- Continuous case, diagonal slices
- Returning to the intro quiz