Class Notes:

1.  Probability (Ch 1)  (pdf)

• 1. Set Theory (Definitions)  (YouTube) 

  2. Set Operations (YouTube) 

  3. Probability Definition and Axioms (YouTube) 

  4.  Joint and Conditional Probability

     • Joint and Conditional Probability (YouTube) 

     • Total Probability and Bayes Theorem (YouTube) 

  5. Independent Events (YouTube) 

  6.  Combined Experiments and Permutations

     • Combined experiments (YouTube)

     • Permutation and Combination (YouTube) 

  7. Bernoulli Trials (YouTube)

2.  Random Variables  (Ch 2) (pdf)

1. 1. Random Variables: definitions and Types (YouTube)

   2. Random Variables CDF and pdf (YouTube)

   3. Gaussian (Normal) R.V. (YouTube)

   4. Gaussian R.V CDF and Q-Function Approximation (YouTube)

   5. Binomial Distribution (Additional Examples of Random Variables) (YouTube)

   6. Poisson, Uniform, Exponential, Rayleigh (Additional Important distributions) (YouTube)

   7. Conditional Density (pdf) and Distribution (CDF) (YouTube)

   8. Range Conditioned Density and Distribution Functions (YouTube)

3. Operation on One Random Variable (Ch3) (pdf)

1. Expectation (YouTube)

2. Moments (YouTube)

   •  Chebyshev and Markov Inequalities (YouTube)

3. Characteristic and Moment Generating Functions (YouTube)

4. Transformation of Random Variables 

   • Monotonic Transformation (YouTube)

   • Nonmonotonic and Discrete Transformation (YouTube)

4. Multiple Random Variables (Ch4) (pdf)

1. Introduction to Vectors of Random Variables and CDF (YouTube)

2. Joint distribution function (YouTube) 

3. Joint density function and properties (YouTube)

4. Conditional distribution and density (YouTube)

5. Statistical Independence (YouTube)

6. Distribution and density of a sum of r.v.’s (YouTube)

7. Central Limit Theorem (Matlab Code) (YouTube)

5. Operation on Multiple  Random Variables (pdf)

1. Expected value of a function of r. v.’s (Matlab Code) (YouTube)

2. Joint characteristic functions (YouTube)

3. Jointly Gaussian r. v.’s  (Matlab Code, results) (YouTube)

4. Transformations of multiple r.v.’s (YouTube)

5. Linear transformations of Gaussian r.v.’s (YouTube)

6. Sampling and some limit theorems (YouTube)

6. Random Processes –Temporal Characteristics (pdf)

1. Concept of a random process (YouTube)

2. Stationary and independence (YouTube)

3. Correlation functions and their properties (YouTube)

4. Gaussian random process (YouTube)

5. Poisson random process (YouTube)

6. Time Averages and Ergodicity (YouTube)

7. Measurement of Correlation Function (YouTube)

7. Random Processes – Spectral Characteristic (pdf)

1. Power Spectral Density and its properties (YouTube)

2. Relationship between PSD and auto-correlation function (YouTube)

8. Linear systems with random inputs (pdf)

1. Random signal response of linear systems (YouTube)

2. Spectral characteristics of system response (YouTube)

9. Introduction to Statistics (pdf)

1. General overview (Video)

2. Sampling and some limit theorems (Video)

3. Point Estimation (Video)

4. Methods of point estimation (MoM & MLE) (Video)

5. Confidence intervals (Video)

   • Confidence intervals on exponential and normal distributions

6. Introduction to hypothesis testing (Video)

10. Review

Additional Links: