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Video course · 15 chapters · 41 min · certificate

Probability & Statistics for Data Science, Machine Learning & AI

Learn the probability and statistics that power data science and AI, from sample spaces and Bayes' theorem to confidence intervals and hypothesis testing. This course walks through random variables, famous distributions, the Central Limit Theorem, estimation, and Bayesian thinking with clear examples.

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What you'll learn

  • Define sample spaces, events, and apply probability rules and counting methods.
  • Calculate conditional probabilities and use Bayes' theorem to update beliefs.
  • Distinguish discrete and continuous random variables using PMFs, PDFs, and CDFs.
  • Describe key distributions (Bernoulli, binomial, Poisson, normal) and their parameters.
  • Explain the Law of Large Numbers, Central Limit Theorem, and sampling distributions.
  • Perform maximum likelihood estimation, confidence intervals, and hypothesis tests.

Chapters

15 chapters · 41:18
  1. 3:36 01Foundations Free preview Sample Spaces & Events Learn to describe randomness through experiments, outcomes, sample spaces, and events.
  2. 2:16 02Rules Members Probability Rules & Counting Learn the axioms of probability, the complement and addition rules, and basic counting.
  3. 2:19 03Conditioning Members Conditional Probability & Independence Update probabilities when you gain new information, and learn when events are independent.
  4. 1:56 04Inference Members Bayes' Theorem Turn conditional probabilities around and update beliefs with evidence using Bayes' theorem.
  5. 2:19 05Distributions Members Random Variables, PMF & PDF Learn discrete and continuous random variables and the functions that describe their probabilities.
  6. 3:56 06Expectation Members Expectation, Variance & Discrete Distributions Compute the mean and spread of distributions, and meet Bernoulli, binomial, and Poisson distributions.
  7. 2:20 07Normal Members Continuous Distributions & the Normal Meet the uniform, exponential, and normal distributions, and learn to standardize with z-scores.
  8. 2:11 08Relationships Members Joint Distributions, Covariance & Correlation Describe how two random variables vary together using joint distributions, covariance, and correlation.
  9. 3:51 09Limit theorems Members Law of Large Numbers & Central Limit Theorem Learn why averages stabilize and why sample averages tend toward a normal distribution.
  10. 4:06 10Summarizing data Members Descriptive Statistics & Sampling Summarize data with center, spread, and shape, and understand samples, estimators, and bias.
  11. 3:38 11Estimation Members Maximum Likelihood & Confidence Intervals Estimate parameters by making observed data most probable, and build intervals for population means.
  12. 2:20 12Testing Members Hypothesis Testing & p-values Test whether effects are real using null hypotheses, test statistics, p-values, and significance levels.
  13. 2:05 13Bayesian Members Bayesian Inference Update a prior belief with data to get a posterior, and connect Bayesian methods to regularized machine learning.
  14. 2:17 14Information Members Entropy, Cross-Entropy & KL Divergence Quantify surprise and information, and see how cross-entropy and KL divergence measure differences between distributions.
  15. 2:08 15Integration Members The Big Picture Connect probability, statistics, and machine learning into one coherent framework.