Introduction to Probability (MATH 203)

2020 Spring
Faculty of Engineering and Natural Sciences
Yunus Sarıkaya, Turgay Bayraktar,
Click here to view.
Formal lecture,Recitation
Task based learning
Click here to view.


Counting techniques, combinatorial methods, random experiments, sample spaces, events, probability axioms, some rules of probability, conditional probability, independence, Bayes' theorem, random variables (r.v.'s), probability distributions, discrete and continuous r.v.'s, probability density functions, multivariate distributions, marginal and conditional distributions, expected values, moments, Chebyshev's theorem, product moments, moments of linear combinations of r.v.'s, special discrete distributions, uniform, Bernouilli, binomial, negative binomial, geometric, hypergeoemtric and Poisson distributions, special probability densities, uniform, gamma, exponential and normal densities, normal approximation to binomial, distribution of functions of r.v.'s, distribution function and moment-generating function techniques, distribution of the mean, law of large numbers, the central limit theorem.


- To give an understanding of uncertainty and randomness
- To teach the fundemantal concepts and defintions of probability
- To equip the students with the tools and techniques of probability theory


Upon completing this course students should be able to:

Use the basic principles of counting, permutations, combinations, and multinomial coefficients.

Perform set operations and compute elementary (conditional) probabilities.
Use the concept of random variables and their distributions, cumulative distribution functions.
Compute marginal distributions, conditional distributions and conditional expectations.
Evaluate mathematical expectations, moments, variances, co-variances, conditional expectations, and moment-generating functions.
Investigate the basic properties of important discrete and continuous random variables such as Bernouilli, binomial, hypergeometric, Poisson, uniform, exponential, gamma and normal.
Implement different techniques such as the distribution function technique, the moment generating function technique, the transformation technique to evaluate the distribution of functions of random variables.
Investigate the properties of various statistics (sample mean, sample variance, order statistics) taken from a population.
See the applications in various disciplines.



2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4





2. Identify, define, formulate and solve complex engineering problems; choose and apply suitable analysis and modeling methods for this purpose. 3







2. Assess how global, national and regional developments affect society. 1

3. Know how to access and evaluate data from various sources of information. 1




1. Design, implement, test, and evaluate a computer system, component, or algorithm to meet desired needs and to solve a computational problem. 1

2. Demonstrate knowledge of discrete mathematics and data structures. 1

3. Demonstrate knowledge of probability and statistics, including applications appropriate to computer science and engineering. 4

1. Provide constructive analysis of economic phenomena at the national and international level, and interactions between the two. 1

2. Develop an understanding of organizations and institutions in the society as well as their influence on the economy. 1

3. Recognize how incentives shape the behavior of individuals and organizations. 1

4. Identify ?economic? problems and propose alternative models and/or design and conduct research to provide viable solutions using theoretical tools and/or quantitative methods. 1

5. Communicate problems and solutions to managerial and policy decision-making units as well as to lay audiences. 1

1. Use mathematics (including derivative and integral calculations, probability and statistics, differential equations, linear algebra, complex variables and discrete mathematics), basic sciences, computer and programming, and electronics engineering knowledge to (a) Design and analyze complex electronic circuits, instruments, software and electronics systems with hardware/software. or (b) Design and analyze communication networks and systems, signal processing algorithms or software 4

1. Comprehend key concepts in biology and physiology, with emphasis on molecular genetics, biochemistry and molecular and cell biology as well as advanced mathematics and statistics. 1

2. Develop conceptual background for interfacing of biology with engineering for a professional awareness of contemporary biological research questions and the experimental and theoretical methods used to address them. 1




1. Analyze global affairs from international relations and economics perspectives. 1

2. Demonstrate theoretical and practical knowledge of the international affairs. 1

3. Compete for increasing opportunities in careers within the newly emerging global institutions. 1

4. Evaluate the international political events and present their views and positions on international affairs with advanced oral and written skills. 1

1. Understand and follow changes in patterns of political behavior, ideas and structures. 1

2. Develop the ability to make logical inferences about social and political issues on the basis of comparative and historical knowledge. 1




  Percentage (%)
Final 40
Midterm 30
Assignment 20
Participation 10



John Freund's Mathematical Statistics with Applications, 8th Edition, Pearson-
Prentice Hall, 2004

Optional Readings

Supplementary Texts :
1) S. Ross: A First Course in Probability, 7th Edition, Pearson- Prentice Hall, 2006.
2) S. Lipschutz: Schaum?s Outline of Theory and Problems of Probability, Mc
Graw-Hill, 2000.