### Introduction to Probability (MATH 203)

2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Yunus Sarıkaya ysarikaya@sabanciuniv.edu, Turgay Bayraktar tbayraktar@sabanciuniv.edu,
Click here to view.
English
Undergraduate
MATH102
Formal lecture,Recitation
Interactive,Task based learning
Click here to view.

### CONTENT

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.

### OBJECTIVE

- 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

### LEARNING OUTCOME

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.

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 35 Midterm 35 Assignment 20 Participation 10

### RECOMENDED or REQUIRED READINGS

 Textbook 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, McGraw-Hill, 2000.