# Theory of Probability and Statistics (MAE531)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ531 5 Theory of Probability and Statistics Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English, reading Course) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes Extension and generalization of concepts taught in MAF331 and MAF43# Creation of a suitable base for deepening the scope of Statistical Science. At the end of the course the student should be able to: Model procedures and situations that occur in everyday reality or in other scientific areas in the Theory of Probability. Understand the basic limit theorems of Probability Theory (laws of large numbers, central limit theorem) and use them for approximating probability calculations. Find the distribution of a function of random variables. Make basic calculations of probability, averages, dispersions, etc., in problems involving randomness with more than one random variable. Working independently Decision-making Production of free, creative and inductive thinking Criticism and self-criticism

### Syllabus

Random vectors-Multivariate distribution function-Joint probability- Joint probability density function. Marginal distributions. Conditional distributions. Special bivariate and multivariate distributions (multinomial, bivariate and multivariate normal etc). Expectation, Variance-Covariance matrix. Moments and Moment generating function of random vector. Distribution of a function of random variables. Order Statistics. Convergence of random variables. Sampling distributions.

### Teaching and Learning Methods - Evaluation

Delivery

Classroom (face-to-face)

Use of Information and Communications Technology -
Teaching Methods