概率论与数理统计英文版总结.doc

Sample?Space??样本空间 The set of all possible outcomes of a statistical experiment is called the sample space. Event 事件 An event is a subset of a sample space. certain event（必然事件）： The sample space itself, is certainly an event, which is called a certain event, means that it always occurs in the experiment. impossible event（不可能事件）： The empty set, denoted by, is also an event, called an impossible event, means that it never occurs in the experiment. Probability of events （概率） If the number of successes in trails is denoted by , and if the sequence of relative frequencies obtained for larger and larger value of approaches a limit, then this limit is defined as the probability of success in a single trial. “equally likely to occur”------probability（古典概率） If a sample space consists of sample points, each is equally likely to occur. Assume that the event consists of sample points, then the probability that A occurs is Mutually exclusive(互斥事件) Definition 2.4.1 Events are called mutually exclusive, if . Theorem 2.4.1 If and are mutually exclusive, then (2.4.1) Mutually independent 事件的独立性 Two events and are said to be independent if Or Two events and are independent if and only if . Conditional Probability 条件概率 The probability of an event is frequently influenced by other events. Definition The conditional probability of , given , denoted by , is defined by if . (2.5.1) The multiplication theorem乘法定理 If are events, then If the events are independent, then for any subset , (全概率公式 total probability) Theorem 2.6.1. If the events constitute a partition of the sample space S such that for than for any event of , (2.6.2) （贝叶斯公式Bayes’ formula.） Theorem 2.6.2 If the events constitute a partition of the sample space S such that for than for any event A of S, , . for