Kodu |
Dersin Adı |
Yarıyıl |
Süresi(T+U) |
Kredisi |
AKTS Kredisi |
MAT207 |
OLASILIK VE İSTATİSTİK |
3 |
3 |
3 |
5 |
DERS BİLGİLERİ |
Dersin Öğretim Dili : |
Türkçe |
Dersin Düzeyi |
BACHELOR'S DEGREE, TYY: + 6.Level, EQF-LLL: 6.Level, QF-EHEA: First Cycle |
Dersin Türü |
Zorunlu |
Dersin Veriliş Şekli |
- |
Dersin Koordinatörü |
Prof. AHMET CİHAT BAYTAŞ |
Dersi Veren Öğretim Üyesi/Öğretim Görevlisi |
Dr.Öğr.Üyesi FERHAT KÜRÜZ-Dr.Öğr.Üyesi SEDA YAMAÇ AKBIYIK |
Ders Ön Koşulu |
Yok |
AMAÇ VE İÇERİK |
Amaç: |
To introduce the basic concepts of probability theory To have the students acquire the skills to analyze nondeterministic signals by modelling them as random processes. |
İçerik: |
Introduction and definitions (Set Theory, Experiment, Sample Space, Events) Mathematical model of probability, Joint and conditional probability, Bayes theorem Independent events and Bernoulli trials The random variable concept Probability distribution and density functions Conditional distributions and densities Expected values, moments and characteristic functions Transformations of a single random variable. Multiple random variables, joint distribution and density functions Limit theorems Operations on multiple random variables Definition of a random process Independence and stationarity Time averages, statistical averages and ergodicity Autocorrelation and cross-correlation functions Gauss and Poisson processes |
DERSİN ÖĞRENME ÇIKTILARI (Öğrenciler, bu dersi başarı ile tamamladıklarında aşağıda belirtilen bilgi, beceri ve/veya yetkinlikleri gösterirler.) |
Know the basic concepts of probability theory. |
Use common probability distributions and analyse their properties. |
Compute conditional probability distributions and conditional expectations. |
Compute distributions by use of transformation techniques and solve problems. |
Define and use the properties of Stochastic processes, especially Gaussian and Poisson Processes. |
HAFTALIK DERS KONULARI VE ÖNGÖRÜLEN HAZIRLIK ÇALIŞMALARI |
Hafta |
Ön Hazırlık |
Konular |
Yöntem |
1 |
- |
Introduction and definitions (Set Theory, Experiment, Sample Space, Events) |
- |
2 |
- |
Mathematical model of probability, Joint and conditional probability, Bayes theorem |
- |
3 |
- |
Independent events and Bernoulli trials |
- |
4 |
- |
The random variable concept |
- |
5 |
- |
Probability distribution and density functions, Conditional distributions and densities |
- |
6 |
- |
Expected values, moments and characteristic functions |
- |
7 |
- |
Transformations of a single random variable |
- |
8 |
- |
MID-TERM EXAM |
- |
9 |
- |
Multiple random variables, joint distribution and density functions |
- |
10 |
- |
Limit theorems, Operations on multiple random variables |
- |
11 |
- |
Random processes and their properties |
- |
12 |
- |
Independence and stationarity of random processes |
- |
13 |
- |
Time averages, statistical averages and ergodicity, Autocorrelation and cross-correlation functions |
- |
14 |
- |
Gauss and Poisson processes |
- |
15 |
- |
Preparation for Final exam |
- |
16 |
- |
FINAL EXAM |
- |
17 |
- |
FINAL EXAM |
- |
KAYNAKLAR |
Mühendislik İstatistiği;Montgomery,Runger,Hubele;Çeviri:Coşkun ÖZKAN,Palme Yayıncılık2017 |
Matemetiksel İstatistik,Mustafa Aytaç, Ezgi yayınları,Ankara Üniv.yayını,1999 |
Örnekleme Teorisi ve işletme yönetiminde uygulaması,Orhan İdil,İ.Ü. Yayını,1980 |
Matemetiksel İstatistiğe giriş,Uğur Korum,Ankara üniversitesi,1971 |
Yönetimde istatistik teknikler ve örnek olaylar, Orhan İdil,İst. Gelişim Üniv. ,1979 |
ÖLÇME VE DEĞERLENDİRME |
Yarıyıl İçi Yapılan Çalışmaların Ölçme ve Değerlendirmesi |
Etkinlik Sayısı |
Katkı Yüzdesi |
Açıklama |
(0) Etkisiz |
(1) En Düşük |
(2) Düşük |
(3) Orta |
(4) İyi |
(5) Çok İyi |
0 |
1 |
2 |
3 |
4 |
5 |
DERSİN PROGRAM ÖĞRENME ÇIKTILARINA KATKISI
KNOWLEDGE |
Theoretical |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to apply mathematics, science and engineering knowledge.
|
|
|
|
|
|
|
KNOWLEDGE |
Factual |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to apply mathematics, science and engineering knowledge.
|
|
|
|
|
|
|
SKILLS |
Cognitive |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to design experiments, conduct experiments, collect data, analyze and interpret results.
|
|
|
|
|
|
|
SKILLS |
Practical |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
A system, product or process has economic, environmental, social, political, ethical, health and safety,
under realistic constraints and conditions such as feasibility and sustainability,
Ability to design to meet requirements.
|
|
|
|
|
|
|
OCCUPATIONAL |
Autonomy & Responsibility |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to work in teams with different disciplines
|
|
|
|
|
|
|
OCCUPATIONAL |
Learning to Learn |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Ability to identify, formulate and solve engineering problems
|
|
|
|
|
|
|
OCCUPATIONAL |
Communication & Social |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
Awareness of having professional and ethical responsibilities.
|
|
|
|
|
|
|
2 |
Ability to communicate effectively verbally and in writing.
|
|
|
|
|
|
|
OCCUPATIONAL |
Occupational and/or Vocational |
|
Program Yeterlilikleri/Çıktıları |
Katkı Düzeyi |
0 |
1 |
2 |
3 |
4 |
5 |
1 |
The ability to have a comprehensive education to understand the impact of engineering solutions on global and social dimensions.
|
|
|
|
|
|
|
2 |
Awareness of the necessity of lifelong learning and the ability to do so.
|
|
|
|
|
|
|
3 |
The ability to have knowledge about current/contemporary issues.
|
|
|
|
|
|
|
4 |
Ability to use the techniques required for engineering applications and modern engineering and calculation equipment.
|
|
|
|
|
|
|
DERSİN İŞ YÜKÜ VE AKTS KREDİSİ |
Öğrenme-Öğretme Etkinlikleri İş Yükü |
Öğrenme-Öğretme Etkinlikleri |
Etkinlik(hafta sayısı) |
Süresi(saat sayısı) |
Toplam İş Yükü |
Lecture & In-Class Activities |
14 |
3 |
42 |
Preliminary & Further Study |
14 |
3 |
42 |
Land Surveying |
0 |
0 |
0 |
Group Work |
0 |
0 |
0 |
Laboratory |
0 |
0 |
0 |
Reading |
0 |
0 |
0 |
Assignment (Homework) |
3 |
5 |
15 |
Project Work |
0 |
0 |
0 |
Seminar |
0 |
0 |
0 |
Internship |
0 |
0 |
0 |
Technical Visit |
0 |
0 |
0 |
Web Based Learning |
0 |
0 |
0 |
Implementation/Application/Practice |
0 |
0 |
0 |
Practice at a workplace |
0 |
0 |
0 |
Occupational Activity |
0 |
0 |
0 |
Social Activity |
0 |
0 |
0 |
Thesis Work |
0 |
0 |
0 |
Field Study |
0 |
0 |
0 |
Report Writing |
0 |
0 |
0 |
Final Exam |
1 |
1 |
1 |
Preparation for the Final Exam |
5 |
3 |
15 |
Mid-Term Exam |
1 |
1 |
1 |
Preparation for the Mid-Term Exam |
5 |
2 |
10 |
Short Exam |
1 |
2 |
2 |
Preparation for the Short Exam |
1 |
3 |
3 |
TOTAL |
45 |
0 |
131 |
|
Genel Toplam |
131 |
|
|
Toplam İş Yükü / 25.5 |
5,1 |
|
|
Dersin AKTS(ECTS) Kredisi |
5,0 |
|