Probability Systems Analysis and Applied Probability

I. Course Overview: MIT OCW – Prof. John Tsitsiklis

Learn probabilistic modeling, random process and statistical inference


II. Course Objective:

A. Conceptual

1. probability model: basic concept

2. translation ability: model in words to mathematical ones

3. bayesian and classical inference: concept and assumption

4. applications of inference models

B. Technical

1. probability distributions

2. conditioning: simplify analysis of complex model

3. probability mass functions, densities and expectations

4. powers of laws of large numbers

5. conditional expectation: concept and role

6. Markov chain: formulate simple dynamic model

7. inference methodology: estimation and hypothesis testing


III. Prerequisite:

A. 18.01 Single Variable Calculus

B. 18.02 Multi Variable Calculus


IV. Why Study Probability?

To think probabilistically is now fundamental ability in science and engineering fields

i.e. quantum mechanics, communication and signal processing, social network

A. Increasing Complexity:

impossible to have perfect model of real world → uncertainty model needed

B. Abundant of Information:

huge information → apply probabilistic modeling and statistical inference must


V. Text Book:

Bertsekas, Dimitri, and John Tsitsiklis. Introduction to Probability. 2nd ed


VI. Plan:

∗ MIT students spend average 11-12 hours each week for lecture, reading and exams