概率论与数理统计英文版总结

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 S 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 n trails is denoted by s , and if the sequence of relative frequencies /s n obtained for larger and larger value of n 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 S consists of N sample points, each is equally likely to occur. Assume that the event A consists of n sample points, then the probability p that A occurs is ( )npP AN Mutually exclusive(互斥事件) Definition 2.4.1 Events 12,,,nA AA are called mutually exclusive, if , ijAAij   . Theorem 2.4.1 If A and B are mutually exclusive, then ()( )( )P ABP AP B (2.4.1) Mutually independent 事件的独立性 Two events A and B are said to be independent if ()( )( )P ABP AP B Or Two events A and B are independent if and only if (| )( )P B AP B. Conditional Probability 条件概率 The probability of an event is frequently influenced by other events. Definition The conditional probability of B , given A , denoted by (|)P B A , is defined by ()(|)( )P ABP B AP A if ( )0P A . (2.5.1) The multiplication theorem 乘法定理 If 12k,,,A AA are events, then 12k121312121()()...