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)

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