INTRO TO PROBABILITY & STATISTICS

SSC 321, Spring 2012
BUR 112, Mon & Wed 3:30 - 5:00 pm

Instructor Pradeep Ravikumar

Office Hours ACES 2.434, Tuesdays 3:30-5:00 pm
TA Christopher Johnson
Recitation Hours ACES x.xxx, Thursdays 1:00-3:00 pm
Overview An introduction to probability and statistics, with practical applications.
First section of the course: fundamentals of probability, counting problems, discrete and continuous random variables, multiple random variables, and limit theorems.
Later section of the course: fundamentals of statistics, Bayesian and classical inference, parameter estimation, confidence intervals, hypothesis testing, and posterior distributions.

Grading 40% Homeworks, 25% Midterm, 30% Final, 5% Class Participation

Textbooks Introduction to Probability, 2nd Ed.. Dimitri P. Bertsekas and John N. Tsitsiklis.

Homeworks

Schedule
Module Date Topic Notes
1: Probability Basics I

 01/18 Sample space, Events, Axioms of probability BT Chap. 1.1-1.2
01/23 Sets, Probability Laws BT Chap. 1.1-1.2
2: Counting/Combinatorics

 01/25 Counting Rules, Permutations, Combinations BT 1.6
01/30 Repetitions, Objects into Boxes BT 1.6
02/01 Counting and Probability BT 1.6
3: Probability Basics II

 02/06 Conditional Probability, Multiplication rule BT 1.3
02/08 Total Probability Theorem, Bayes Rule BT 1.4
02/13 Independence: Given two events, Conditional independence BT 1.5
02/15 Independence: Given a collection of events, Pairwise Independence BT 1.5
4: Discrete Random Variables

02/20 Discrete Random Variables, Probability Mass Function (PMF), Functions of Random Variables BT 2.1-2.3
02/22 Expectation, Variance, Conditional PMF (given event), Cond. Expectation BT 2.4
02/27 Total Expectation Theorem, Joint PMF, Conditional PMF BT 2.5, 2.6
02/29 Independent Random Variables BT 2.5, 2.7
03/05 Review BT Chap. 1, 2
03/07 Midterm BT Chap. 1, 2
03/12 Spring Break
03/14 Spring Break
5: Continuous Random Variables

03/19 Continuous Random Variables, Probability distribution function, Cumulative distribution functions, Normal Random Variables BT 3.1-3.3
03/21 Multiple Random Variables: Joint PDFs, Conditioning, Independence BT 3.4-3.5
03/26 Conditional PDF, Continuous Bayes Rule BT 3.5-3.6
03/28 Review
6: Advanced Probability

04/02 Covariance, Correlation, Conditional Expectation BT 4.2-4.3
04/04 Conditional Expectation and Variance Contd. BT 4.3
04/09 Sum of Random Number of Random Variables, Transforms BT 4.4-4.5
6: Bayesian Statistical Inference

04/11 Intro to Statistics, Bayesian Inference BT 8.1
04/16 MAP Rule, Conditional Expectation Estimator BT 8.2-8.3
7: Classical Statistical Inference

04/18 Maximum Likelihood Estimation, Desirable Properties of Estimators BT 9.1
04/23 Estimating the mean and variance of a random variable, Confidence Intervals BT 9.1
04/25 Hypothesis Testing BT 9.3
04/30 Review of Statistics
05/02 Review of Probability