Probability theory is the study of reasoning with incomplete information. The laws of logic govern all correct reasoning when operating under conditions of perfect information. If is true, and if implies , then we may deduce that is true as well. But in many cases, we may be uncertain about whether is true or not. Probability theory governs all correct reasoning when operating under conditions of incomplete or unreliable information. As such, it is an extremely useful field of study, with many applications.
Fundamental concepts edit
Probabilities on finite sets edit
- Finite probability spaces
- Random variables on finite probability spaces
- Sums of independent random variables on finite probability spaces
Probability and measure theory edit
Laws of large numbers edit
Central limit theorems edit
Partition Functions edit
- von Mises, Richard (1964). Mathematical Theory of Probability and Statistics. New York and London: Academic Press.
- Kolmogorov, Andrey (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer.
- Itô, Kiyosi (1984). Introduction to probability theory. Cambridge u.a., Univ. Pr.
- Kallenberg, Olav (1997). Foundations of modern probability. New York: Springer.
- Loève, Michel (1963). Probability Theory I. D. van Nostrand.