What you need to know about Bayes' Rule, Probability Density Functions, Marginal/Conditional Probs

We cover the basic ideas of probability theory from probability density functions (i.e. functions that tell us how likely different events are to occur) to conditional and marginal probability distributions. The focus is on a pedagogical presentation over a strictly rigorous one. Each idea is presented with the context of specific examples and then generalized.
The final example uses data from: www.medrxiv.org/content/10.11... . This is not intended to be medical advice as the numbers do not come from a trusted peer reviewed resource and I am not a doctor. Take it only as an example of Bayes' rule in action.
00:00:00 - Introduction
00:01:46 - Conditional Probabilities
00:05:21 - Probability Density Functions
00:11:00 - PDFs Over Multiple Variables
00:17:10 - Marginal Distributions
00:22:42 - Independent Random Variables
00:28:46 - Dependent Random Variables
00:33:49 - Bayes' Rule
00:36:14 - Intuition Behind Bayes' Rule
00:45:03 - More Formal Treatment of Bayes' Rule
00:49:51 - Example Problem 1
00:51:52 - Example Problem 2
00:55:48 - Solution for Problem 1
00:59:34 - Solution for Problem 2
01:08:04 - Final Example: Tests of Infection
Errata:
21:35, the answer should read 7/72
A note on naming: the "proper name" for a PDF over a discrete variable is a Probability Mass Function

[@aliassaf8782]

Pretty important content. I'm supporting this channel.

[@casualscience]

Thank you very much Ali, I really appreciate that!

[@casualscience]

Errata: 21:35, the answer should read 7/72 A note on naming: the "proper name" for a PDF over a discrete variable is a Probability Mass Function