Probability theory

Probability theory is a branch of mathematical science that deals with the mathematical analysis of random events. Probability is commonly used to describe the mind’s attitude to statements that we are not sure of. Statements usually take the form of “Will a particular event occur?” and the attitude of our minds will be of the form “How confident are we that this event will occur?” Our confidence can be described numerically, which is a value between 0 and 1 that we call probability. The more likely to occur an event is, the more confident we are that it will occur. The focus in this chapter is mainly on probability space, random variable, multi-dimensional probability distribution, expected value, variance, and covariance.