SDS321: Introduction to Probability and Statistics
The course syllabus can be found here.
The office hours are Tuesdays 11:30-12:30 at GDC 7.306.
The course textbook is by Dimitri Bertsekas and John Tsitsiklis. Introduction to Probability. 2nd ed. Athena Scientific, 2008. ISBN: 978188652923. The first chapter is available online here. An excellent resource is the lecture notes and videos available here. We will also follow Sheldon Ross's A First Course in Probability (edition 8th) for some worked out problems.
Lecture notes
01/19 : Overview, logistics, and axioms of probability. [Slides] . Quiz can be found [Here]
01/21 : Axioms of probability and Conditional probability. [Slides] . Readings 1.1-1.3 of B/T.
01/26 : Conditional probability. [Slides]
01/28 : Bayes rule. [Slides]
02/02 : Statistical independence. [Slides]
02/04 : Conditional independence and intro to counting. [Slides]
02/09 : Counting 2. [Slides]
02/11 : Counting 2.0.1 and discrete random variables. [Slides]
02/16 : Discrete random variables- last lecture contd. [Slides: read upto-page 21]
02/18 : Expectation and variance [Slides]
02/22 : Expectation and variance [Slides]
02/28 : Review for midterm [Slides]
03/2 : Midterm I
03/7 and 03/9 : Joint distributions, conditional PMF and Independence [Slides]
03/21 : Continuous random variables- introduction [Slides]
03/23 : Continuous random variables- Uniform, Exponential, Normal [Slides]
03/28 : Continuous random variables- Standardization, Joint PDF [Slides]
03/30 : Continuous random variables- Conditional PDF, Bayes Rule [Slides]
04/5 : Continuous random variables- Conditional expectation, Independence, [Slides]
04/7 : Continuous random variables- Independence, Covariance and correlation, Function of R.V's [Slides]
04/9 : Continuous random variables- Review [Slides]
04/18 : Continuous random variables- Derived distributions and functions of two random variables [Slides]
04/20 : Continuous random variables- Functions of two random variables, conditional expectation and starting Statistics [Slides]
04/25 : Statistics: Central Limit Theorem [Slides]
04/27 : Statistics: Maximum Likelihood estimation [Slides]
05/2 : Statistics: Maximum Likelihood estimation completed and confidence intervals [Slides]
05/4 : Statistics: Significance testing [Slides]
Readings
Set algebra, conditional probability, Bayes' rule, independence 1.1-1.5 (Bertsekas Tsitsiklis)
Combinatorics: Ross Chapter 1
Discrete r.v. 2.1-2.2 (Bertsekas-Tsitsiklis)
Discrete r.v. PMF's of Binomial, Bernoulli and Poisson 2.3 (Bertsekas-Tsitsiklis)
Discrete r.v. Expectation and variance 2.4 (Bertsekas-Tsitsiklis)
Discrete r.v. Joint distributions, conditioning, total expectation theorem 2.5-2.6 (Bertsekas-Tsitsiklis)
Continuous r.v. pdf, cdf, normal distribution, exponential, joint distributions, conditioning, derived distribution 3.1-3.6 (Bertsekas-Tsitsiklis)
Multiple r.v.'s: covariance and correlation (B-T 4.5), conditional expectation as a r.v. (B-T 4.3-4.4)
Markov and Chebyshev inequalities, Weak Law of Large Numbers and the CLT (B-T chapter 5.1-5.4)
Maximum Likelihood Estimates, Biased/Unbiased estimators and Confidence intervals (B-T chapter 9.1)
Significance testing (B-T chapter 9.4)
Practice problems
Homework 2 from last time OLD HW2 solutions
Practice midterm and [solutions]
Midterm 2015 solutions. Ignore problem 2 and 3 since they are about continuous distributions.
Midterm 2016 solutions
Combinatorics practice problem set and solutions .
MIDTERM 1 solutions and Histogram. Mean 20.1, Median 22.25, Standard dev 4.81.
MIDTERM 2 solutions and Histogram. Mean 20.6, Median 22, Standard dev 4.5.
Midterm 2 2016 (Leave 4b out. We have not done that yet.) solutions 1 a) has answer 0.16
Final 2 2016 - Solve problems 3,4 and 7 solutions
Continuous R.V. practice problems and solutions
How to pattern match [Here] . Tips and tricks [here]
Continuous r.v. review here .
Discrete and continuous and Stat practice problems [problems] [solutions] .
Final 1 2016 Here and Solutions
Final 2 2016 solutions
Midterm 2-until now review here .
Homeworks
Homework 1 . Due on Thursday, Jan 26th by 5pm via canvas. Solutions.
Homework 2 . Due on Thursday, February 2nd by 5pm by Canvas. Solutions.
Homework 3 . Due on Thursday, February 9th by 5pm by Canvas. Solutions.
Homework 4 . Due on Friday, February 17th by 5pm via Canvas. Solutions.
Homework 5 . Due on Friday, February 24th by 5pm via Canvas. Solutions.
Homework 6 . Due on Tuesday,Match 10th by midnight via canvas. Solutions.
(Pseudo) Homework . Some practice integration problems and reading Solutions.
Homework 7. Due Friday March 31st by midnight via Canvas Solutions.
Homework 8. Due Friday April 7th by midnight via Canvas Solutions.
Homework 9. Due Friday April 28th by midnight via Canvas Solutions.
Extra credit HW. Due Friday May 5th by midnight via Canvas Solutions.
Homework 10. Due Friday May 7th by midnight via Canvas Solutions.