Probability_and_Statistics
back to Mathematics -- Science
: Probability Axioms -- Probability Theory -- Probability Applications -- Probability Distributions
: Statistical Theory -- Applied Statistics -- Planning Research -- Summarizing Statistical Data -- Interpreting Statistical Data
Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. In any case, we measure the uncertainty of events on a scale from zero (impossible events) to one (certain events or no uncertainty).
Probability Axioms form the basis for mathematical Probability Theory. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. Probability Applications include even more than Statistics, which is usually based on the idea of Probability Distributions.
Probability Theory plays a critical role in the development of Statistical Theory. Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to
There are some Sciences which use statistics so extensively and have specialized terminology that we recognize special disciplines like:
Some valuable resources on the Web are: