Probabilistic Systems Analysis and Applied Probability

Course Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Lecture Notes:

SES #	TOPICS ( Click  to download Pdf Slides)
L1	Probability Models and Axioms (PDF)
L2	Conditioning and Bayes' Rule (PDF)
L3	Independence (PDF)
L4	Counting Sections (PDF)
L5	Discrete Random Variables; Probability Mass Functions; Expectations (PDF)
L6	Conditional Expectation; Examples (PDF)
L7	Multiple Discrete Random Variables (PDF)
L8	Continuous Random Variables - I (PDF)
L9	Continuous Random Variables - II (PDF)
L10	Continuous Random Variables and Derived Distributions (PDF)
L11	More on Continuous Random Variables, Derived Distributions, Convolution (PDF)
L12	Transforms (PDF)
L13	Iterated Expectations (PDF)
L13A	Sum of a Random Number of Random Variables (PDF)
L14	Prediction; Covariance and Correlation (PDF)
L15	Weak Law of Large Numbers (PDF)
L16	Bernoulli Process (PDF)
L17	Poisson Process (PDF)
L18	Poisson Process Examples (PDF)
L19	Markov Chains - I (PDF)
L20	Markov Chains - II (PDF)
L21	Markov Chains - III (PDF)
L22	Central Limit Theorem (PDF)
L23	Central Limit Theorem (cont.), Strong Law of Large Numbers (PDF)