Statistics 110: Probability

Is this course completely free to access?

Yes, all core materials are completely free. The full lecture series is available on YouTube with 34 video lectures, the course website provides handouts and strategic practice problems with solutions, and the second edition of the textbook “Introduction to Probability” by Blitzstein and Hwang is freely available online at probabilitybook.net. The edX version (Stat110x) with interactive features and animations is also free to audit, though you can optionally pay for a verified certificate. Print copies of the textbook are available for purchase through CRC Press or Amazon if you prefer a physical book, but the free online version is complete.

What mathematical background do I need before starting?

You should have a solid foundation in single-variable calculus, including derivatives, integrals, and infinite series. The course assumes you’re comfortable with mathematical notation and can work with summations, limits, and basic integration techniques. Some familiarity with linear algebra is helpful but not strictly required. The course is designed for Harvard undergraduates who have completed calculus, so while mathematically rigorous, it doesn’t assume prior probability or statistics knowledge. If you’re comfortable with calculus and willing to engage with mathematical concepts deeply, you’ll be well-prepared.

What topics are covered in this course?

The course provides comprehensive coverage starting with probability basics including sample spaces, events, conditional probability, and Bayes’ Theorem. You’ll learn about discrete and continuous random variables and their distributions including Binomial, Negative Binomial, Geometric, Poisson, Uniform, Normal, Exponential, Beta, and Gamma distributions. Advanced topics include expectation and variance, moment generating functions, joint and conditional distributions, independence, covariance and correlation, transformations and convolutions, order statistics, conditional expectation, probability inequalities, the Law of Large Numbers, the Central Limit Theorem, chi-square and Student’s t-distributions, the multivariate normal distribution, and Markov chains. The course emphasizes both theoretical understanding and practical applications across science, engineering, economics, and everyday decision-making.

How long does it take to complete this course?

The 34 video lectures are approximately 50-60 minutes each, totaling around 30-35 hours of video content. However, to truly master the material, you should expect to invest significantly more time working through practice problems, reading the textbook, and solving problem sets. Most dedicated learners spend 10-12 weeks working through the course at 10 hours per week, similar to Harvard’s semester-long format. The self-paced nature allows you to adjust the timeline, but probability concepts build on each other, so rushing through without mastering fundamentals can make later material challenging.

What makes Professor Blitzstein’s teaching style special?

Professor Blitzstein is renowned for making probability intuitive and engaging through storytelling, real-world examples, and what he calls “thinking probabilistically.” He emphasizes understanding over memorization, building deep intuition for why formulas work rather than just applying them mechanically. His lectures are filled with memorable examples, clever mnemonics, and connections between seemingly disparate concepts. He frequently uses humor and encourages students to develop probabilistic thinking as a way of understanding the world. His genuine enthusiasm for the subject is infectious, and he has a remarkable ability to explain subtle concepts clearly while maintaining mathematical rigor. Many students describe his lectures as transformative in how they think about uncertainty and randomness.

Will I receive a certificate for completing this course?

YouTube lectures and the course website materials don’t offer certificates. However, the edX version (Stat110x) provides a verified certificate of completion if you pay the certificate fee (auditing remains free). The certificate demonstrates you’ve completed the coursework and assessments, which can be valuable for your resume or academic portfolio. For Harvard students taking the course for credit, it fulfills degree requirements. The knowledge and problem-solving skills you gain are the most valuable outcomes, as this course forms the foundation for advanced work in statistics, machine learning, data science, quantitative finance, and many other fields.

How does this course prepare me for statistics and data science?

This course provides the essential probabilistic foundations underlying all of statistics, machine learning, and data science. You’ll develop the ability to think rigorously about uncertainty, randomness, and inference—skills crucial for understanding statistical methods, building predictive models, designing experiments, and making data-driven decisions. The course teaches you to model real-world phenomena probabilistically, understand sampling distributions, and grasp why statistical procedures work. Topics like conditional probability, expectation, distributions, and the Central Limit Theorem are fundamental to techniques like hypothesis testing, regression, Bayesian inference, and machine learning algorithms. Many data scientists and statisticians credit this course with providing the deep conceptual understanding that allows them to use advanced methods correctly and develop new approaches when needed, making it invaluable preparation for graduate studies or careers in quantitative fields.