Review Of Univariate Probability

Probability is a universally accepted tool for expressing degrees of confidence or doubt about some proposition in the presence of incomplete information or uncertainty. By convention, probabilities are calibrated on a scale of 0 to 1; assigning something a zero probability amounts to expressing the belief that we consider it impossible, whereas assigning a probability of one amounts to considering it a certainty. Most propositions fall somewhere in between. Probability statements that we make can be based on our past experience, or on our personal judgments. Whether our probability statements are based on past experience or subjective personal judgments, they obey a common set of rules, which we can use to treat probabilities in a mathematical framework, and also for making decisions on predictions, for understanding complex systems, or as intellectual experiments and for entertainment. Probability theory is one of the most applicable branches of mathematics. It is used as the primary tool for analyzing statistical methodologies; it is used routinely in nearly every branch of science, such as biology, astronomy and physics, medicine, economics, chemistry, sociology, ecology, finance, and many others. A background in the theory, models, and applications of probability is almost a part of basic education. That is how important it is.