Phase 2: Probability & Statistics · ~75 minutes · Python
Probability and Distributions
Probability is the language AI uses to express uncertainty.
Hiring signal: Understanding of probability and distributions internals
What you will learn
- Implement PMFs and PDFs from scratch for Bernoulli, categorical, Poisson, uniform, and normal distributions
- Compute expected value, variance, and use the Central Limit Theorem to explain why Gaussians dominate
- Build softmax and log-softmax functions with the numerical stability trick (subtract max logit)
- Calculate cross-entropy loss from logits and connect it to negative log-likelihood
Introduction
Type: Learn Language: Python Prerequisites: Phase 1, Lessons 01-04 Time: ~75 minutes
Learning Objectives
- Implement PMFs and PDFs from scratch for Bernoulli, categorical, Poisson, uniform, and normal distributions
- Compute expected value, variance, and use the Central Limit Theorem to explain why Gaussians dominate
- Build softmax and log-softmax functions with the numerical stability trick (subtract max logit)
- Calculate cross-entropy loss from logits and connect it to negative log-likelihood
Unlock the full lesson
You've read the first 2 sections. The rest of this lesson covers The Problem, The Concept, Build It, Use It, Exercises, Key Terms, Further Reading — plus a hands-on lab, quiz, and project artifact.
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