Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
ADVANCED PROBABILITY THEORY FOR ENGINEERS BSM 601 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. NİLÜFER YURTAY Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To teach the students probability and stochastis processes at an advanced level together with important applications Dersin İçeriği Introduction, Probability Spaces, Experiments, Outcomes, Events, Conditional Probability, Independence, Compound Experiments, Binomial Distribution, Poisson Distribution, Conditional Probabilities in Digital Communications, Probability Distributions, Conditional Distributions, Functions of a Random Variables, Expected Values, Joint Distributions of Pairs of Random Variables, Conditional Distributions of Pairs of Random Variables, Jointly Gaussian Random Variables, Functions of Two Random Variables, Transformation of a Pair of Random Variables, Multivariate Probability Distributions, Multivariate Conditional Distributions, Distributions of Functions of Multiple Random Variables, Expected Values, The Multivariate Gaussian Distribution, Estimating Parameters of a Distribution, The Central Limit Theorem
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Learning both foundations and applications of the subject 1 - 2 - 4 - 6 - 8 - 12 - 14 - 15 - 16 - A - C - D -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 6:Motivations to Show 8:Group Study 12:Case Study 14:Self Study 15:Problem Solving 16:Project Based Learning Ölçme Yöntemleri: A:Testing C:Homework D:Project / Design

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction, Probability Spaces, Experiments, Outcomes, Events, Conditional Probability
2 Independence, Compound Experiments, Binomial Distribution, Poisson Distribution, Conditional Probabilities in Digital Communications
3 Probability Distributions, Conditional Distributions
4 Functions of a Random Variables, Expected Values
5 Joint Distributions of Pairs of Random Variables
6 Conditional Distributions of Pairs of Random Variables, Jointly Gaussian Random Variables
7 Functions of Two Random Variables, Transformation of a Pair of Random Variables
8 Multivariate Probability Distributions, Multivariate Conditional Distributions
9 Distributions of Functions of Multiple Random Variables, Expected Values
10 The Multivariate Gaussian Distribution, Estimating Parameters of a Distribution
11 The Central Limit Theorem, Random Sums
12 Probabilistic Description of Stochastic Processes Expected Values and Autocovariance Functions, Ergodicity
13 Poisson Affiliated Stochastic Processes, Transformations of Stochastic Processes
14 Noise: White Noise, Thermal Noise, Shot Noise, Applications Related to Reducing the effects of Noise.

#### Kaynaklar

Ders Notu Probability and Stochastic Processes for Engineers / Carl W. Helstrom, 1984
Ders Kaynakları Introduction to Stochastic Processes / Paul G. Hoel, Sidney C. Port, Charles J. Stone, 1972
Probability, Random Variables, and Stochastic Processes / Athanasios Papoulis, 1991
Kalman Filtering [Theory and Practice] / Mohinder S. Grawal, Angus P. Andrews, 1993
Lessons in Estimation Theory for Signal Processing, Communications, and Control / Jerry M. Mendel, 1995

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 ability to complete and implement “limited or incomplete data” by using the scientific methods. X
2 ability to consolidate engineering problems, develop proper method(s) to solve and apply the innovative solutions to them X
3 ability to develop new and original ideas and method(s), to develop new innovative solutions at design of system, component or process X
4 gain comprehensive information on modern techniques, methods and their borders which are being applied to engineering X
5 ability to design and apply analytical, modelling and experimental based research, analyze and interpret the faced complex issues during the design and apply process X
6 gain high level ability to define the required information and data X
7 ability to work in multi-disciplinary teams and to take responsibility to define approaches for complex situations X
8 systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
9 aware of social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation and announcement X
10 aware of new and developing application of profession and ability to analyze and study on those applications X
11 ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 40
KisaSinav 1 20
Odev 1 20
KisaSinav 2 20
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 1 10 10
Final examination 1 20 20
Toplam İş Yükü 141
Toplam İş Yükü /25(s) 5.64
Dersin AKTS Kredisi 5.64
; ;