Theory of Probability


Stanford School of Humanities and Sciences




This course covers probability spaces as models for phenomena with statistical regularity. Students who take this course should be able to use the framework of probability to quantify uncertainty and update beliefs given the right evidence. Students will also learn how to use a variety of strategies to calculate probabilities and expectations, both conditional and unconditional, as well as how to understand the generative stories for discrete and continuous distributions and recognize when they are appropriate for real-world scenarios.

Students who take the course for 4 units should expect to complete an additional assignment, and those who take the course for 5 units should expect to complete two additional assignments and a midterm exam. 


Integral Calculus of Several Variables (Stanford Course: MATH 52) and familiarity with infinite series, or equivalent.

A conferred Bachelor’s degree with an undergraduate GPA of 3.3 or better.

Topics include

  • Naive and axiomatic definition of probability
  • Conditional probability such as Bayes' rule, independence of events and Simpson's paradox
  • Bernoulli, Binomial, and Hypergeometric distributions
  • Indicator r.v.s, continuous random variables and exponential distribution
  • Poisson distribution, approximation and process
  • Inequalities such as Cauchy-Schwarz, Jensen, Markov, Chebyshev and Chernoff

Course Availability

The course schedule is displayed for planning purposes – courses can be modified, changed, or cancelled. Course availability will be considered finalized on the first day of open enrollment. For quarterly enrollment dates, please refer to our graduate education section.

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