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()()...
