Phase 2: Probability & Statistics · ~75 minutes · Python

Probability and Distributions

Probability is the language AI uses to express uncertainty.

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: Earlier lessons in this course
Time: ~75 minutes

Objective

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, Check Yourself, Key Terms & Next — plus a hands-on lab, quiz, and project artifact.

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