Dersin Bilgileri

Dersin Adı	Türkçe	Olasılık Teorisi
	İngilizce	Probability Theory
Dersin Kodu	MAT 221E	Kredi	Ders (saat/hafta)	Uygulama (saat/hafta)	Labratuvar (saat/hafta)
Dönem	2	3	3	-	-
Dersin Dili		İngilizce
Dersin Koordinatörü		Burhaneddin İzgi
Dersin Amaçları		1. To provide the basic concepts of probability 2. To set up probability models for a range of random phenomena, both discrete and continuous
Dersin Tanımı		Combinatorial methods; product rule, permutation, combination, binomial expansion, multinomial expansion, tree diagram, generating function. Probability; experiment, sample space, sigma algebra, probability axioms, conditional probability, Bayes theorem. Random variable and probability function; basic definitions, cumulative distribution function, expected value, Chebyshev inequality, the law of large numbers, moment generating function, z transformation-probability generating function, multi dimensional random variables, conditional distributions, correlation, regression. Discrete and continuous distributions, Poisson's event. Fokker-Plank equation. The function of random variable; F -distribution, t distribution, chi-square distribution. Characteristic function; properties, inverse transformation formula, central limit theorem. Markov chains; Markov property, Markov chain, canonic form, regular stochastic matrix, regular Markov chain, ergodic chain
Dersin Çıktıları		Student, who passed the course satisfactorily can: I. Understand and apply basic concepts of probability. II.Set up probability models for a range of random phenomena, both discrete and continuous. III. Use probability distribution and probability densities. IV. Evaluate Mathematical Expectation. V. Use special probability distribution and probability densities. VI. Use Markov chains.
Önkoşullar
Gereken Olanaklar
Diğer		https://www.mathavuz.itu.edu.tr/mat/catalog.php?code=MAT221
Ders Kitabı		Salih Çelebioğlu ve Reşat Kasap (Sheldon M. Ross dan Çeviri) (2015) Olasılık ve İstatistiğe Giriş. Nobel Akademik Yayıncılık. John E. Freund’s Mathematical Statistics with Applications Irwin Miller,Marylees Miller 7th edition,Pearson Prentice Hall, 2004
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