| Area of Mathematics: | Statistics-Probability-Operational Research | ||
| Semester: | 3ο | ||
| Course ID: | 31304 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 3 | Practice: 2 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Bobotas Panayiotis | ||
Description
- Elements of Combinatorics: Counting of discrete formations. Counting principles. Permutations, combinations with and without replacement. Factorials, Binomial and Multinomial coefficients. Inclusion-exclusion principle. Stirling’s formula. Partition problems.
- Random experiment and sample point. Sample space and events. Definition of probability, mutually exclusive events, classical definition of probability. Limiting relative frequency, geometric probability, empirical probability. Axiomatic definition of probability. Conditional probability. Restriction of sample space and Multiplication Rule. Theorem of Total Probability and Bayes Theorem. Independent events.
- Random variables and distribution function.
- Discrete random variables. Probability function. Mean, variance and moments of discrete random variables. Markov and Chebyshev inequalities.
- Uniform, binomial, geometric and hypergeometric distribution, negative binomial distribution, Poisson distribution, other basic discrete distributions.
- Continuous random variables. Density function. Mean, variance and moments of continuous random variables.
- Continuous univariate distributions. Uniform, exponential and normal distribution. Gamma and Beta distribution, other basic continuous distributions. Approximation of the binomial by the normal distribution.
- Moment generating functions and probability generating functions of unidimensional distributions.
- Weak law of large numbers.
Bibliography
Ross S. A first course in Probability. Pearson. 2020
