Probability Theory

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$A$ is true, and if $A$ implies $B$, then we may deduce that $B$ is true as well. But in many cases, we may be uncertain about whether $A$ 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

1. Probability spaces
2. Conditional probability
3. Independence
4. Random variables

Probabilities on finite sets

5. Finite probability spaces
6. Random variables on finite probability spaces
7. Sums of independent random variables on finite probability spaces

Sources

• 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.