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Probability for Data Scientists

Pro

Conditional probability, random variables, the distribution zoo, joint distributions, Bayes theorem, and the limit theorems (LLN & CLT).

8 modules · Module 1 is free; Modules 2+ require Pro.

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What this course covers

A module-by-module concept outline. Open the course to learn each topic with animated explanations, in-browser code, practice challenges, and a knowledge check.

Module 1. The Language of Uncertainty

Free
Topics
What P=0.7 Actually MeansSample Spaces & EventsThe Three AxiomsSet Operations on EventsCounting PrinciplesMeet the Streamora Dataset
Sections
  1. 1What Does P = 0.7 Actually Mean?
  2. 2Sample Spaces & Events — Meet Streamora
  3. 3The Three Axioms of Probability
  4. 4Set Operations — Union, Intersection, Complement
  5. 5Counting Principles — Permutations & Combinations
  6. 6When Probability Is (and Isn't) the Right Tool

Module 2. Conditional Probability

Pro
Topics
What Changes When You Know SomethingThe Multiplication RuleTree Diagrams as a Thinking ToolIndependence (and Its Common Abuse)The Chain RuleStreamora Case: User Retention Cohorts
Sections
  1. 1What Changes When You "Know Something"
  2. 2The Conditional Probability Formula
  3. 3The Multiplication Rule & Tree Diagrams
  4. 4Independence — Formal Definition & Common Traps
  5. 5The Chain Rule for Multiple Events
  6. 6Streamora Case: Conditional Watch-Through Rates

Module 3. Bayes' Theorem

Pro
Topics
The Belief-Updating FormulaPrior, Likelihood, PosteriorThe Disease-Test ParadoxIterative Updating with EvidenceBayes in Spam Filters & RecommendationsWhy Base Rates Trick Smart People
Sections
  1. 1Bayes' Theorem — The Belief-Updating Formula
  2. 2Prior, Likelihood, Posterior — The Three Pieces
  3. 3The Disease-Test Paradox (The Famous Gotcha)
  4. 4Iterative Updating — One Piece of Evidence at a Time
  5. 5Bayes in the Wild — Spam Filters & Streamora Recommendations
  6. 6The Base-Rate Fallacy — Why Smart People Miss This

Module 4. Random Variables

Pro
Topics
From Events to NumbersDiscrete vs ContinuousPMF, PDF, and CDFExpectation as Center of MassVariance — The SpreadLinearity of Expectation
Sections
  1. 1From Events to Numbers — What Is a Random Variable?
  2. 2Discrete vs Continuous — The Mental Model Shift
  3. 3PMF, PDF, and CDF — Three Views of the Same Thing
  4. 4Expectation — The Center of Mass
  5. 5Variance & Standard Deviation — The Spread
  6. 6Linearity of Expectation — The Most Useful Theorem

Module 5. The Distribution Zoo

Pro
Topics
Choosing the Right DistributionBernoulli & Binomial — Yes/No at ScaleGeometric — Time Until First SuccessPoisson — Rare Events Per Unit TimeUniform & ExponentialThe Normal Distribution
Sections
  1. 1The Decision Tree — Which Distribution Fits?
  2. 2Bernoulli & Binomial — Did They Click?
  3. 3Geometric — How Long Until First Success?
  4. 4Poisson — Streamora Viewer Arrivals
  5. 5Uniform & Exponential — The Continuous Twins
  6. 6The Normal Distribution — Why It's Everywhere
  7. 7Streamora Case: Picking Distributions for Real Metrics

Module 6. Joint Distributions & Dependence

Pro
Topics
Two Random Variables at OnceJoint, Marginal & ConditionalIndependence — Formal DefinitionCovariance & CorrelationThe Correlation-Causation TrapConditional Expectation E[Y|X]
Sections
  1. 1Two Random Variables at Once — The Joint Picture
  2. 2Marginal & Conditional Distributions
  3. 3Independence — The Formal Definition
  4. 4Covariance & Correlation — How Variables Move Together
  5. 5The Correlation-Causation Trap (and Simpson's Paradox)
  6. 6Conditional Expectation E[Y|X] — The Best Single Prediction

Module 7. The Limit Theorems

Pro
Topics
The Law of Large NumbersThe Central Limit TheoremWhy n=30 Matters (and Why It's Not Magic)CLT in Action — Streamora Watch-TimeThe Bridge to Statistics
Sections
  1. 1The Law of Large Numbers — Frequencies Converge
  2. 2The Central Limit Theorem — Averages Go Normal
  3. 3Why n=30 Matters (and When It Doesn't)
  4. 4CLT in Action — Averaging Streamora Watch-Time
  5. 5The Bridge to Statistics — Confidence Intervals Preview

Module 8. Probability in the Wild

Pro
Topics
Maximum Likelihood EstimationThe MLE Recipe — The Coin ExampleMonte Carlo SimulationBootstrap — Resampling from Your DataWhere Probability Lives in ML
Sections
  1. 1Maximum Likelihood Estimation — The Idea
  2. 2The MLE Recipe — The Coin-Flipping Example
  3. 3Monte Carlo Simulation — Estimating π & Streamora KPIs
  4. 4Bootstrap — Resampling from Your Own Data
  5. 5Where Probability Lives in ML — LLM Sampling, Model Confidence

Ready to start Probability for Data Scientists?

Module 1 is free. Unlock the full course with Pro.

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All course syllabi

SQL FundamentalsSQL MasterySQL Window FunctionsPython FundamentalsPandas FundamentalsStatistics for Data ScienceMachine Learning Fundamentals (scikit-learn)A/B Testing & ExperimentationLLM Foundations