| Area of Mathematics: | Statistics-Probability-Operational Research | ||
| Semester: | 4ο | ||
| Course ID: | 41303 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 3 | Practice: 2 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Panayiotis Bobotas | ||
Description
- Fundamental axioms of probability. Definition of a random variable and a random vector.
- Bidimensional random variable and distribution function. Discrete and continuous bidimensional random variables. Joint distribution function, marginal distribution function. Multidimensional random variables, multidimensional distributions, discrete multidimensional random variables, continuous multidimensional random variables.
- Multidimensional means, covariance, variance-covariance matrix, (linear) correlation coefficient. Conditional distributions, conditional mean, law of total expectation. Independence of random variables. Regression curve.
- Functions of random variables, distribution of sums of independent random variables, transformations of distributions, convolutions of distributions.
- Samples and sampling. X2, t and F distributions.
- Basic multidimensional distributions and their properties (Multinomial, bivariate and multivariate normal etc)
- Moment generating functions and probability generating functions of multidimensional random variables.
- Ordered random variables.
- Convergence of a sequence of random variables, types of convergence, limit theorems (laws of large numbers, Central Limit Theorem etc).
Bibliography
Ross S. A first course in Probability. Pearson. 2020
Roussas G. A first course in Mathematical Statistics. Academic Press. 1997
