Probability and Statistics

Upon successful completion of this course, you will:

At a conceptual level:

• Master the basic concepts associated with probability models .
• Be able to translate models described in words to mathematical ones.
• Understand the main concepts and assumptions underlying Bayesian and classical inference .
• Obtain some familiarity with the range of applications of inference methods .

At a more technical level:

• Become familiar with basic and common probability distributions .
• Learn how to use conditioning to simplify the analysis of complicated models.
• Have facility manipulating probability mass functions , densities , and expectations .
• Develop a solid understanding of the concept of conditional expectation and its role in inference.
• Understand the power of laws of large numbers and be able to use them when appropriate.
• Become familiar with the basic inference methodologies (for both estimation and hypothesis testing ) and be able to apply them.
• Acquire a good understanding of two basic stochastic processes (Bernoulli and Poisson) and their use in modeling.
• Learn how to formulate simple dynamical models as Markov chains and analyze them.