Syllabus
1. Random event with finitely many outcomes, classical probability.
2. Combinatorial probability.
3. Geometric probability, Bertrand's paradox.
4. Independence of random events, conditional probabilities, Bayes' theorem, medical diagnosis, Simpson's paradox.
5. Discrete random variable, its distribution, expectation.
6. Problems of calculating the expectation.
7. Random walk, gambler's ruin.
8. Records, their expected number, waiting time for the next record.
9. Optimization problems, partner selection problem.
10. Normal distribution, limit theorems.
Annotation
Introduction to discrete probability and solutions of interesting problems by simple probabilistic and statistical methods. An elective course for 1st year students of General and Financial Mathematics.