Probability for Data Scientists.

The foundation. What probability actually measures, sample spaces, events, the three axioms, set operations, counting — and the Streamora running dataset.

1What Does P = 0.7 Actually Mean?

Sections

2Sample Spaces & Events — Meet Streamora

3The Three Axioms of Probability

4Set Operations — Union, Intersection, Complement

5Counting Principles — Permutations & Combinations

6When Probability Is (and Isn't) the Right Tool

Module 2: Conditional Probability

What changes when you know something? Multiplication rule, tree diagrams, independence (and where it lies to you), the chain rule.

1What Changes When You "Know Something"

Sections

2The Conditional Probability Formula

3The Multiplication Rule & Tree Diagrams

4Independence — Formal Definition & Common Traps

5The Chain Rule for Multiple Events

6Streamora Case: Conditional Watch-Through Rates

Module 3: Bayes' Theorem

The belief-updating formula. Prior, likelihood, posterior. The disease-test paradox done right. Spam filters and Streamora recommendations.

1Bayes' Theorem — The Belief-Updating Formula

Sections

2Prior, Likelihood, Posterior — The Three Pieces

3The Disease-Test Paradox (The Famous Gotcha)

4Iterative Updating — One Piece of Evidence at a Time

5Bayes in the Wild — Spam Filters & Streamora Recommendations

6The Base-Rate Fallacy — Why Smart People Miss This

Module 4: Random Variables

From events to numbers. PMF, PDF, and CDF. Expectation as the center of mass. Variance. The most useful theorem you’ll learn this year (linearity of expectation).

60 min

1From Events to Numbers — What Is a Random Variable?

Sections

2Discrete vs Continuous — The Mental Model Shift

3PMF, PDF, and CDF — Three Views of the Same Thing

4Expectation — The Center of Mass

5Variance & Standard Deviation — The Spread

6Linearity of Expectation — The Most Useful Theorem

Module 5: The Distribution Zoo

Bernoulli, Binomial, Geometric, Poisson, Uniform, Exponential, Normal. Stop memorizing — learn the decision tree for picking the right one.

1The Decision Tree — Which Distribution Fits?

7 sections

Sections

2Bernoulli & Binomial — Did They Click?

3Geometric — How Long Until First Success?

4Poisson — Streamora Viewer Arrivals

5Uniform & Exponential — The Continuous Twins

6The Normal Distribution — Why It's Everywhere

7Streamora Case: Picking Distributions for Real Metrics

7 sections

Module 6: Joint Distributions & Dependence

Intermediate

Two random variables at once. Independence (the formal version). Covariance, correlation, the causation trap, and Simpson’s paradox.

1Two Random Variables at Once — The Joint Picture

Sections

2Marginal & Conditional Distributions

3Independence — The Formal Definition

4Covariance & Correlation — How Variables Move Together

5The Correlation-Causation Trap (and Simpson's Paradox)

6Conditional Expectation E[Y|X] — The Best Single Prediction

Module 7: The Limit Theorems

Intermediate

Why averages go Normal no matter what. The Law of Large Numbers, the Central Limit Theorem, why n=30 matters — and the bridge to Statistics.

1The Law of Large Numbers — Frequencies Converge

5 sections

Sections

2The Central Limit Theorem — Averages Go Normal

3Why n=30 Matters (and When It Doesn't)

4CLT in Action — Averaging Streamora Watch-Time

5The Bridge to Statistics — Confidence Intervals Preview

5 sections

Module 8: Probability in the Wild

Intermediate

Maximum Likelihood Estimation, Monte Carlo simulation, the bootstrap. Where probability quietly powers everything — from spam filters to LLM token sampling.