1 — 01/27 |
Lecture 0, Lecture 1 |
Course Overview, Basic Concepts in Probability, Probability Models |
1 |
2 — 02/03 |
Lecture 2 |
Review of Probability: Set theory, Probability Spaces |
2 |
3 — 02/10 |
Lecture 2, Lecture 2A |
Computing Probabilities Using Counting Methods, Replacement, and Ordering |
2 |
4 — 02/17 |
Lecture 3 |
Conditional Probability, Bayes' Rule, Independence, Generation of Random Numbers |
2 |
5 — 02/24 |
Lecture 3 |
More on Bayes' Rule, Independence, and Real-World Examples |
2 |
6 — 03/03 |
Lecture 4 |
Discrete Random Variables: Notion of a Random Variable, Probability Mass Functions (PMF), Expected
Value, Moments, Important Discrete Random Variables, Generation of Discrete Random Variable |
3 |
7 — 03/10 |
Mid-Term Exam |
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8 — 03/17 |
Spring Break |
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9 — 03/24 |
Lecture 4 |
Discrete Random Variables: Notion of a Random Variable, Probability Mass Functions (PMF), Expected Value,
Moments, Important Discrete Random Variables, Generation of Discrete Random Variables |
3 |
10 — 03/31 |
Lecture 5 |
Continuous Random Variables: Cumulative Distribution Functions (CDF), Probability Density Functions (PDF),
Moment of a Random Variable, Mean and Variance of Continuous Random Variables |
4 |
11 — 04/07 |
Lecture 6 |
Discrete Random Variables: Cumulative Distribution Functions (CDF), Probability Mass Functions (PMF),
Mean and Variance of Discrete Random Variables |
4 |
12 — 04/14 |
Lecture 6 |
Functions of Random Variables, Expectations and Characteristic Function, Markov and Chebychev Inequalities |
4 |
13 — 04/21 |
Lecture 7 |
Two Random Variables: Marginal Probability Mass Function, Joint CDF, Joint PDF, Conditional Distributions
and Independence, Expected Value of a Function of Two Random Variables, Expectations and Correlations, Pairs
of Jointly Gaussian Random Variables, Generating Jointly Gaussian Random Variable |
5 |
14 — 04/28 |
Lecture 8 |
Random Vectors: Functions of Several Random Variables, Expected Value of Vector Random Variables, Jointly
Gaussian Random Vectors, and Convergence of Random Sequences |
6 |
15 — 05/05 |
Lecture 9 |
Stochastic Processes: Basic concepts, Covariance, correlation, and stationarity, Gaussian processes and Brownian
motion, Poisson and related processes, Power spectral density, Stochastic processes and linear systems |
9 |
16 — 05/12 |
Final Exam |
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