| Week |
Topics |
Chapter
Section of Bertsekas/Tsitsiklis |
Quiz or Exam? |
| 1 |
Introduction, Set Theory,
Axioms, Probability models Conditional Probability |
1.1-1.3 |
|
| 2 |
Total Probability, Bayes rule Independence |
1.4-1.5 |
|
| 3 |
Independent trials (binomial) Network reliability Counting Problems + Recap |
1.6 |
Quiz - Monday |
| 4 |
Discrete random variables: PMF Functions of a single r.v. Expectation, mean, variance |
2.1-2.4 |
|
| 5 |
Cumulative Distribution Function
(CDF) Joint discrete random variables, joint PMF |
2.5 |
Quiz |
| 6 |
Conditional PMF Independence, Bayes rule Problems + Recap |
2.6-2.8 |
|
| 7 |
Continuous random variables,
PDF, CDF Midterm Exam 1 |
3.1-3.2 |
Midterm
Exam
1: Feb 27. Syllabus: Chap 1, 2.1-2.3 |
| 8 |
Gaussian PDF Conditioning on an event Joint PDF |
3.3-3.4 |
|
| 9 |
Conditioning on a r.v.:
Conditional PDF, CDF Bayes rule for continous r.v.'s Independence |
3.5 |
|
| 10 |
Derived distributions Problems + Recap |
3.6 |
|
| 11 |
MGF, sums of random variables Covariance, correlation, conditional expectation |
parts of chapter 4 |
|
| 12 |
Least squares estimation and
linear LSE Midterm Exam 2 |
parts of chapter 4 | Midterm
Exam 2: April 3 Syllabus: Chapter 1 and 2 |
| 13 |
Problems + recap Markov, Chebyshev inequalities Weak law of large numbers Central limit theorem |
parts of chapter 7 |
|
| 14 |
Introduce Monte Carlo and
Importance Sampling Introduce Markov chains |
Notes will be posted parts of Chapter 6 |
|
| 15 |
Finish discussing Markov Chains Problems + Recap |
||
| Exam week |
Final Exam |