확률과정론

강의상세

This course provides a broad introduction to probability theory and random processes and their applications to engineering problems.

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.