How to think about uncertainty and randomness
How to make good predictions
The story approach to understanding random variables
Common probability distributions used in statistics and data science
Methods for finding the expected value of a random quantity
How to use conditional probability to approach complicated problems
Probability and statistics help to bring logic to a world replete with randomness and uncertainty. This course will give you tools needed to understand data, science, philosophy, engineering, economics, and finance. You will learn not only how to solve challenging technical problems, but also how you can apply those solutions in everyday life.
With examples ranging from medical testing to sports prediction, you will gain a strong foundation for the study of statistical inference, stochastic processes, randomized algorithms, and other subjects where probability is needed.
Unit 0: Introduction, Course Orientation, and FAQ
Unit 1: Probability, Counting, and Story Proofs
Unit 2: Conditional Probability and Bayes' Rule
Unit 3: Discrete Random Variables
Unit 4: Continuous Random Variables
Unit 5: Averages, Law of Large Numbers, and Central Limit Theorem
Unit 6: Joint Distributions and Conditional Expectation
Unit 7: Markov Chains
Familiarity with U.S. high school level algebra concepts; Single-variable calculus: familiarity with matrices. derivatives and integrals.
Not all units require Calculus, the underlying concepts can be learned concurrently with a Calculus course or on your own for self-directed learners.
Units 1-3 require no calculus or matrices; Units 4-6 require some calculus, no matrices; Unit 7 requires matrices, no calculus.
Previous probability or statistics background not required.