Probability theory and Mathematical statistics (chapter One basic concepts of probability theory)

Note: This article only records chapter concepts and is used to recall knowledge systems. Reference book "Probability Theory and Mathematical Statistics Fourth Edition".
Chapter One basic concept of probability theory random test (with three characteristics) sample space, random event sample space sample point random Event (event) event occurrence basic event inevitable event impossibility event (∅) event relationship with the event of the Operation Equality and event (A∪B) product event (ab,a∩b ) Difference event (A-B) incompatible (mutually exclusive) inverse events (opposing events) commutative law, binding law, distribution rate, de-Morgan Law frequency and probability frequency frequency (three basic properties) probability probability (non-negative, normative, can be added) other properties (finite additive, inverse event probability, addition formula, etc.) possible probability (classical approximate type) and other possible types (classical approximate: two features) the actual inference principle of the probability formula of hypergeometric distribution is supplemented by the probability conditional probability of geometrical approximate condition (P (b| A), the probability of event B occurring under the condition of event a) multiplication principle P (AB) =p (b| A) · P (A) Promotion: P (ABC) =p (c| AB) · P (b| A) · P (A)
Full probability formula and Bayesian Formula Division (complete event Group) full probability formula (often used to find the probability of event a occurring based on the probability of known "partitioning") Bayesian (Bayes) formula