Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
PROBABİLİTY THEORY AND RANDOM VARİABLES EEM 586 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Dr.Öğr.Üyesi GÖKÇEN ÇETİNEL Dersi Verenler Dersin Yardımcıları Arş. Gör. Burhan Baraklı Dersin Kategorisi Dersin Amacı We usually have to use statistical models in real systems since we can not know, compute, or measure all forces that affect an event. The objective of this course is to teach student how statistical methods are used for analyzing physical systems, especially communication systems. Dersin İçeriği Introduction to probability, random variables, functions of random variables, random vectors, expected value, random processes, statistical signal processing applications
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Understanding the concept of a random variable 4 - 5 - 9 - 12 - A - C - D - 2 - Learning computation of a probability density function of a random variable generated from another random variable 4 - 5 - 9 - 12 - A - C - D - 3 - Discussing convergence of random sequences 4 - 5 - 9 - 12 - A - C - D - 4 - Learning random processes 4 - 5 - 9 - 12 - A - C - D - 5 - Investigating statistical signal processing applications of probability 4 - 5 - 9 - 12 - A - C - D -
 Öğretim Yöntemleri: 4:Drilland Practice 5:Demonstration 9:Simulation 12:Case Study Ölçme Yöntemleri: A:Testing C:Homework D:Project / Design

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction to probability theory, probability axioms, definitions of conditional and total probability, condition for independence, applications of Bayes theorem
2 Introducing random variable, probability distribution and density functions, examples of discrete and continuous random variables
3 Obtaining probability density function of random variable obtained from another random variable
4 Expected value of a random variable, conditional expected value and moments
5 Chebyshev and Schwartz inequalities, Chernoff bound, moment generating function and characteristic function
6 Joint distribution and density for random vectors, functions of random vectors
7 Expected value vector and covariance matrix for random vectors, properties of covariance matrices, characteristic function computation for random vectors
8 Definition of a random process
9 Some important random processes
10 Computation of probability distribution and density function of a random variable in terms of those of a random variable applied to a linear, time-invariant system
11 Definition of a wide sense stationary random process, vector random processes and state variables representation
12 Estimation of random variables, Kalman and Wiener filtering applications
13 Expectation-maximization algorithm and its applications in signal processing
14 Spectrum estimation

Ders Notu
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
2 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
3 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
4 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
5 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
6 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
7 High level ability to define the required information, data and reach, assess. X
8 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
9 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
10 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
11 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
12 Ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment. X
13 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
14 Ability; to Access to wide and deep information with scientific researches in the field of Engineering, evaluate, interpret knowledge and implement. X
15 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
16 Ability; To complete and implement “Limited or incomplete data” by using the scientific methods. To stick knowledge of different disciplinarians together. X
17 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
18 Ability; to consolidate engineering problems, develop proper method to solve and apply innovative solutions. X
19 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
20 Ability; To develop new and original ideas and methods, To develop new innovative solutions at design of system, component or process X
21 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
22 Comprehensive information on modern techniques, methods and their borders which are being applied to engineering. X
23 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
24 Ability; to design and apply analytical, modeling and experimental based research, analyze and interpret the faced complex issues during the design and apply process. X
25 High level ability to define the required information, data and reach, assess. X
26 High level ability to define the required information, data and reach, assess. X
27 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
28 Ability; To lead multi-disciplinary teams To take responsibility to define approaches for complex situations. X
29 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
30 Systematic and clear verbal or written transfer of the process and results of studies at national and international environments X
31 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
32 Social, scientific and ethical values guarding adequacy at all professional activities and at the stage of data collection, interpretation, announcement. X
33 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
34 Awareness at new and developing application of profession and ability to analyze and study on those applications. X
35 Ability to interpret engineering application’s social and environmental dimensions and it’s compliance with the social environment. X
36 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 30
Odev 1 3
PerformanGoreviLabaratuvar 1 20
PerformansGoreviSeminer 1 20
Odev 2 3
Odev 3 3
Odev 4 3
Odev 5 3
Odev 6 3
Odev 7 3
Odev 8 3
Odev 9 3
Odev 10 3
Toplam 100
Yıliçinin Başarıya Oranı 60
Finalin Başarıya Oranı 40
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 2 32
Mid-terms 10 7 70
Quiz 1 5 5
Assignment 1 10 10
Oral Examination 1 10 10
Performance Task (Laboratory) 1 15 15
Toplam İş Yükü 190
Toplam İş Yükü /25(s) 7.6
Dersin AKTS Kredisi 7.6
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