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.

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

What You Need to Succeed

• A conferred Bachelor’s degree with an undergraduate GPA of 3.3 or better
• Integral calculus of several variables (MATH 52) and familiarity with infinite series, or equivalent

What You Need To Get Started

Before enrolling in your first graduate course, you must complete an online application.

Don’t wait! While you can only enroll in courses during open enrollment periods, you can complete your online application at any time.

Once you have enrolled in a course, your application will be sent to the department for approval. You will receive an email notifying you of the department's decision after the enrollment period closes. You can also check your application status in your mystanfordconnection account at any time.

Learn more about the graduate application process.

How Much It Will Cost

Learn more about tuition and fees.