| BIL 1004 | Probability and Statistics | 3+0+1 | 4 | ||||
| Year / Semester | Spring semester | ||||||
| Level of Course | First Cycle | ||||||
| Status | Compulsory | ||||||
| Department | Computer Engineering | ||||||
| Prerequisites and co-requisites | N/A | ||||||
| Mode of Delivery | Face to face | ||||||
| Contact hours | 14 weeks | ||||||
| Lecturer | Asst. Prof. Dr. Murat Aykut | ||||||
| Co-Lecturer | |||||||
| Language of instruction | Turkish | ||||||
| Internship | N/A | ||||||
| Course Syllabus | |||||||
| Week | Subject | Related Notes / Files | |||||
| Week 1 | Basic Concepts: Stochastic process, sample space, event, certain event, impossible event; Basic operations on events; Probability Models in Discrete Sample Spaces; Traditional Probability Model | ||||||
| Week 2 | Basic axioms of probability theory and basic results from these axioms | ||||||
| Week 3 | Geometric probability; Conditional probability; Multiplication of Probabilities; Independence of Events; Bayes formula | ||||||
| Week 4 | Random variable and its characteristics: Concept, basic characteristics | ||||||
| Week 5 | Distribution of random variables; cumulative distribution function; Probability (density) function; Basic characteristics of a distribution function | ||||||
| Week 6 | Classification of distributions: discrete distributions (Bernoulli, Binomial, Geometric, Poisson), continuous distributions (uniform, exponential, gauss, Gamma, Erlang, Chi-square, Rayleigh, Weibull) | ||||||
| Week 7 | The expected value of the random variable; Expected value properties | ||||||
| Week 8 | Variance and standard deviation of random variable; Basic characteristics of variance | ||||||
| Week 9 | Midterm exam | ||||||
| Week 10 | Multivariate distribution functions; Mixed distributions, quantile function; median | ||||||
| Week 11 | Bivariate distribution functions; Marginal distributions; Conditional distributions | ||||||
| Week 12 | A statitics application: Bayes Classifier | ||||||
| Week 13 | Histogram; Moments; Center Moments; Skewness; Kurtosis; Moment Generating Functions; Covariance; correlation | ||||||
| Week 14 | Estimation; Maximum likelihood estimation; Biased / unbiased estimations; MAP estimation; Bayes estimation | ||||||
| Week 15 | Regression; Confidence interval | ||||||
| Week 16 | Final exam | ||||||
| Textbook / Material | |||||||
| 1 | Probability and Statistics for Engineering and the Sciences 9th Edition - Jay L. Devore, Brooks Cole, 9 edition, 2015, 792 pages | ||||||
| Recommended Reading | |||||||
| 2 | Probability and statistics 4th Edition - Morris H. DeGroot, Pearson, 4 edition, 2011, 912 pages. | ||||||
| 3 | Statistics 12th Edition - James T. McClave, Terry T. Sincich, Pearson, 12 edition, 2012, 840 pages | ||||||
All announcements will be made, and resources will be shared via course Piazza page (join as a student to class "BİL 1004").