END213

School of Engineering \ Industrial Engineering

3

5

Compulsory

Turkish

-

Industrial Engineering; Biomedical Engineering

Sample space; The classical definition of probability; Algebra and Sigma algebras; Axioms of probability theory; Geometric and Conditional probability; Independent events; Total probability formula; Bayes theorem; Definition of random variable and distribution function; Classification of distributions; Joint and Marginal distributions; Definition, basic properties and applications of Expected Value, Variance and Moments; Moment generating and characteristic functions and types of convergence, Law of Large Number and Central Limit Theorem

1. R.E. Walpole, R.H. Myers, S.L. Myers, K. Ye, “Probability and Statistics for Engineers and Sciences”, 8th Edition, Pearson Prentice Hall, New Jersey, 2007.
2. S. Ross, A First Course in Probability, Ed.8, Pearson Prentice Hall, New Jersey 2010.
3. Cevdet Cerit ve M. Yüksel, “Olasılık”, İTÜ yayınları,
4. Fikri Akdeniz, “Olasılık ve İstatistik “, Nobel Kitapevi, 2016.
5. T. Khaniyev vd., “Olasılık kuramında Çözümlü Problemler”, Nobel Yayın Evi, 2018.

1. Be able to express basic probability concepts and axioms
2. Knowing Geometric and Conditional probability; Independent events; Be able to express the total probability formula and Bayes theorem
3. Knowing the definition of random variable and its distribution function and classifying distributions
4. Ability to interpret the definition and basic properties of expected value and variance
5. Definition and applications of moments; Knowing moment generating and characteristic functions and types of convergence.

1. Acquires the ability to learn and apply the fundamentals of classical probability theory,
2. Acquires the ability to define and apply the probability characteristics of random variables,
3. Acquires the ability to define and apply the numerical characteristics of random variables.

Week 1: General information about the development process of probability theory; Stochastic experiment; Sample space; Concept of random event; Classical definition of probability
Week 2: Algebra and Sigma algebras; Axioms and basic corollaries of probability theory
Week 3: Geometric probability; Conditional probability; Independent events; multiplication rule
Week 4: Total probability formula; Bayes theorem and its applications
Week 5: Definition and basic properties of random variables; Distribution and Distribution function of random variable
Week 6: Basic properties of the distribution function; Classification of distributions
Week 7: Distribution of the function of a random variable
Week 8: Joint and Marginal Distributions; Independence of random variables
Week 9: Definition and basic properties of expected value
Week 10: Definition and basic properties of variance
Week 11: Definition and applications of moments; Moment generating and characteristic functions
Week 12: Types of convergence; Law of Large Numbers; Central Limit Theorem

• Midterm 40 %
• Final 50 %
• Homework 10 %