Probability

Events, Bayes, random variables, distributions and the covariance matrix that PCA and anomaly detection both need.

Module 01.4 · Beginner
Free

8h · 12 lessons · 1 challenge

Before this: Calculus & Optimization

About this module

Probability is where a loss function comes from. Cross-entropy is not a formula someone chose; it is what falls out of maximum likelihood, and this module builds to that.

It also covers the material the later modules quietly depend on: joint and conditional distributions, covariance, the covariance matrix and the multivariate Gaussian, which PCA and anomaly detection both need and which nothing else here teaches.

After this module you can

12 lessons

Lesson 1
1Sample spaces, events and conditional probability
Kind
Concept
Length
45 min
Lesson 2
2Bayes rule and the base rate trap
Kind
Concept
Length
45 min
Lesson 3
3Bayes Duel: beat your intuition on medical tests
Kind
Interactive
Length
30 min
Lesson 4
4Random variables and probability distributions
Kind
Concept
Length
45 min
Lesson 5
5Discrete distributions: Bernoulli, binomial, Poisson
Kind
Concept
Length
40 min
Lesson 6
6Continuous distributions: PDF, CDF, uniform and Gaussian
Kind
Concept
Length
45 min
Lesson 7
7Expectation, variance and standard deviation
Kind
Concept
Length
45 min
Lesson 8
8Joint, marginal and conditional distributions
Kind
Concept
Length
45 min
Lesson 9
9Covariance, correlation and the covariance matrix
Kind
Concept
Length
45 min
Lesson 10
10The multivariate Gaussian
Kind
Concept
Length
40 min
Lesson 11
11Maximum likelihood, and cross-entropy falling out of it
Kind
Concept
Length
50 min
Lesson 12
12Checkpoint: name that likelihood
Kind
Checkpoint
Length
25 min

The challenge: Bayes Duel

Ten medical-test scenarios where intuition and arithmetic disagree. Commit to a number before the answer shows.

Worth 350 XP.

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