Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
PROBABILITY IST 401 7 3 + 1 4 5
Ön Koşul Dersleri Students are assumed to be familiar with Analysis I-II-III-IV
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. ÖMER FARUK GÖZÜKIZIL Dersi Verenler Prof.Dr. ÖMER FARUK GÖZÜKIZIL Dersin Yardımcıları Research Assistants from Applied Mathematics. Dersin Kategorisi Dersin Amacı To show probability theory and its relation of events. Dersin İçeriği Basic concepts and terminology, set theory and sample space, permutation and combination,probability, random variables and their functions, some discrete distributions, some continious distributions.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she recalls set theory, permutation and combination 1 - 2 - 3 - 4 - 14 - 15 - A - C - 2 - He/she uses the rules of probability 1 - 2 - 3 - 4 - 14 - 15 - A - C - 3 - He/she uses random variables and their functions. 1 - 2 - 3 - 4 - 14 - A - C - 4 - He/she summarizes expected value, Variance and moments. 1 - 2 - 3 - 4 - 14 - A - C - 5 - He/she restates distributions of random variables. 1 - 2 - 3 - 4 - 14 - A - C - 6 - He/she restates some discrete distributions. 1 - 2 - 3 - 4 - 14 - A - C - 7 - He/she restates some continuous distributions. 1 - 2 - 3 - 4 - 14 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Set theory, sample space, Counting tecniques, permutation and combination. [1] pages 9-36
2 Repeated combination, Binom Theorem [1] pages 41-55
3 Introduction to probability, some rules of probability, Conditional Probability, Bayes´ theorem. [1] pages 59-80
4 Random variables and distributions of discrete and continuous random variables. [1] pages 121-126
5 Bivariate random variables [1] pages 132-140
6 Expected value and variance of a random variable. Moments and moment generating funtions. [1] pages 140-160
7 Functions of random variables [1] pages 170-177
8 Midterm exam
9 Some discrete distributions: Bernoulli , binomial , multinomial, geometric, negative binomial [1] pages 189-203
10 Some discrete distributions: uniform, Poisson, Hypergeometric [1] pages 206-216
11 Some continuous distributions: the normal distribution [1] pages 231-235
12 The normal distribution as an aproximation to the binomial distribution [1] pages 241-247
13 Some continuous distributions: uniform, exponential, gamma, beta [1] pages 254-259
14 Relations between distributions [1] pages 259-260

#### Kaynaklar

Ders Notu [1] Fikri AKDENİZ, Olasılık ve İstatistik, Nobel kitabevi, Adana, 2004.
Ders Kaynakları [2] Meyer, P. L. (1973). Introductory probability and statistical applications. Massachusetts:Addison-Wesley Publishing Company.
[3] Maden S. Olasılığa giriş, Seçkin kitabevi. ankara 2006
[4] Ö.Faruk GÖZÜKIZIL ve Metin Yaman, Olasılık Problemleri, Sakarya Kitabevi, 2005.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
KisaSinav 3 10
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 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 5 5
Quiz 3 3 9
Performance Task (Laboratory) 0 0 0
Final examination 1 10 10
Toplam İş Yükü 136
Toplam İş Yükü /25(s) 5.44
Dersin AKTS Kredisi 5.44
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