Random Variables as Types - Lecture 11

Explore the concept of random variables as types in this lecture from MIT's Computational Thinking Spring 2021 course. Delve into Gaussian distributions, theoretical random variables vs. sampling, and the benefits of defining abstract types for random variables. Learn how to define a type for a Gaussian random variable and understand the sum of two Gaussian random variables. Discover probability distributions, sampling techniques, and more general distributions. Investigate adding random variables, generic programming for sums, and the χ₁² distribution. Conclude with an exploration of using symbolics in computational thinking. Follow along with timestamped sections to navigate key topics throughout the 51-minute lecture.

Syllabus

Introduction.
Concepts for today.
Random variables as types.
Random variables.
Gaussian distributions.
Sum of two Gaussians.
Theoretical random variables vs. sampling.
Why define a type at all?.
Defining abstract types for random variables.
Defining a type for a Gaussian random variable.
Sum of two Gaussian random variables.
Probability distribution of a Gaussian.
Sampling from a Gaussian distribution.
More general distributions.
Adding two random variables.
Generic programming: sum.
χ₁² distribution.
Using symbolics.