**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