http://math.uni-pannon.hu/~szalkai/Illustrative-PrTh-1.pdf 181102 Illustrative Probability Theory by István Szalkai, Veszprém, University of Pannonia, Veszprém, Hungary The original "Hungarian" deck of cards, from 1835 Note: This is a very short summary for better understanding. N and R denote the sets of natural and real numbers, □ denotes the end of theorems, proofs, remarks, etc., in quotation marks ("...") we also give the Hungarian terms /sometimes interchanged/. Further materials can be found on my webpage http://math.uni-pannon.hu/~szalkai in the Section "Valószínűségszámítás". dr. Szalkai István,
[email protected] Veszprém, 2018.11.01. Content: 0. Prerequisites p. 3. 1. Events and the sample space p. 5. 2. The relative frequency and the probability p. 8. 3. Calculating the probability p. 9. 4. Conditional probability, independence of events p. 10. 5. Random variables and their characteristics p. 14. 6. Expected value, variance and dispersion p. 18. 7. Special discrete random variables p. 21. 8. Special continous random variables p. 27. 9. Random variables with normal distribution p. 29. 10. Law of large numbers p. 34. 11. Appendix Probability theory - Mathematical dictionary p. 37. Table of the standard normal distribution function () p. 38. Bibliography p. 40. Biographies p. 40. 2 0. Prerequisites Elementary combintorics and counting techniques. Recall and repeat your knowledge about combinatorics from secondary school: permuta- tions, variations, combinations, factorials, the binomial coefficients ("binomiális együtthatók") n n(n 1)...(n k 1) k k! and their basic properties, the Pascal triangle, Newton's binomial theorem. The above formula is defined for all natural numbers n,kN .