Advanced Probability For Discrete Systems

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Not Required

Course Contents

Probability spaces, random variables, expectation, conditional expectation, stochastic convergence, characteristic functions, and limit theorems. Introduction to Markov and Gaussian processes, stationary processes, spectral representation, ergodicity, renewal processes, martingales, and applications to estimation, prediction, and queueing theory.

Weekly Schedule

1) Probability Space, Axioms, and Theorems
2) Discrete Random Variables: Distributions, Statistics
3) Function of Random Variable
4) Joint and marginal distributions
5) Correlation, covariance, moment generating functions
6) Limit Theorems
7) Central limit theorem, Gaussian distribution, bivariate distribution
8) Midterm Exam
9) Markov chains: basic definitions, state transition diagram and matrix representation
10) Markov chains: balance equations and applications
11) Introduction to queuing theory and some applications
12) Martingale
13) Estimation: sample mean, sample variance, properties of estimation
14) MMSE and LLSE estimation
15) Kalman and Wiener Filtering
16) Final Exam

Recommended or Required Reading

Planned Learning Activities and Teaching Methods

1) Lecture
2) Discussion
3) Demonstration
4) Group Study
5) Problem Solving

Assessment Methods and Criteria

Contribution of Semester Studies to Course Grade	60%
Number Percentage Semester Studies Midterm Examination 1 70% Quiz 5 30%
Contribution of Final Examination to Course Grade	40%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required