Axiomatic definition of probability, independent events, conditional probabilities, Bayes theorem, combinatorial analysis, discrete and continuous random variables, distribution functions, distributions of special interest: Bernoulli, binomial, Poisson, uniform, exponential, normal, Gamma, Weibull. Joint distribution functions, independent random variables, conditional distributions, moment generating functions, limit theorems, central limit theorem, strong law of large numbers. Descriptive statistics.

After the successful fulfilment of the course, the student: -will have a deep and working knowledge of the basic notions of Probability theory, Combinatorics and Statistics as these are described in the course syllabus,

• will have the knowledge to interpret various mathematical models within Probability theory and a solid conceptual and technical background for further study and investigation,
• will have the ability to compute probabilities and various quantities of a one-dimensional or a multi-dimensional random variable, such as its distribution function, the expected value or the variance,
• will have the ability to recognize well-known discrete and continuous probability distributions and to interrelate them with real problems of practical interest,
• will have the ability though the foundations of Statistics to use the methodology of the basic estimating parameters and to perform calculations.

Not required.

Μ. Κούτρα, Θεωρία Πιθανοτήτων και Εφαρμογές, Εκδ. Σταμούλης.

Τ. Δάρας και Π. Σύψας, Πιθανότητες και Στατιστική, Θεωρία και Εφαρμογές, Εκδ. Ζήτη.

Systematic development and explanation of the theory (and through examples), methods of solutions of exercises, solutions of exercises in the teaching hours and in the problem session hours, final written exam.

Homeworks, tests, final written exam.

Face-to-face.