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Probability models and axioms
Conditioning and Bayes' rule
Independence
Counting
Discrete random variables; probability mass functions; expectations
Discrete random variable examples; joint PMFs
Multiple discrete random variables: expectations, conditioning,
independence
Continuous random variables
Multiple continuous random variables
Continuous Bayes rule; derived distributions
Derived distributions; convolution; covariance and correlation
Iterated expectations; sum of a random number of random variables
Bernoulli process
Poisson process - I
Poisson process - II
Markov chains - I
Markov chains - II
Markov chains - III
Weak law of large numbers
Central limit theorem
Bayesian statistical inference - I
Bayesian statistical inference - II
Classical statistical inference - I
Classical inference - II
Classical inference - III
a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example:
- The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science".
- A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions.
- Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget.
The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.
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