1. |
|
1. Sample Space and Probability
|
Set theory, Sample Space, Probability Axioms, Some Consequences of the Axioms. |
|
2. |
|
2. Discrete Random Variables
|
Discrete Random Variables: PMF, CDF, Expectation, Variance and Standard Deviation, Joint PMF, Conditioning, Independence. |
|
3. |
|
3. Continuous Random Variables
|
General Random Variables: CDF, PDF, and Gaussian RV's, Joint PDF, Continuous Conditioning. |
|
4. |
|
4. Further Topics on Random Variables
|
Further Topics on Random Variables: Derived Random Variables, Covariance and Correlation, Conditional Expectation and Variance, Transforms, Sums of Independent Random Variables. |
|
5. |
|
5. Limit Theorems
|
Limit Theorems: Markov and Chebyshev Inequalities, The Weak Law of Large Numbers, Convergence in Probability, The Central Limit Theorem. |
|
6. |
|
6. The Bernoulli and Poisson Processes
|
Stochastic Processes: Bernoulli and Poisson Random Processes. |
|
7. |
|
7. Bayesian Statistical Inference
|
Bayesian Statistical Inference: Point Estimation, Hyothesis Testing, MAP, Least Mean Square Estimation. |
|
8. |
|
8. Classical Statistical Inference
|
Non-Bayesian Statistical Inference: Linear Regression, Binary Hypothesis Testing, Significance Testing. |
|
9. |
|
9. Classical Statistical Inference
|
Non-Bayesian Statistical Inference: Linear Regression, Binary Hypothesis Testing, Significance Testing. |
|