概率论与数理统计英文版总结(word版可编辑修改)
概率论与数理统计英文版总结(word版可编辑修改)
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概率论与数理统计英文版总结(word版可编辑修改)
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
p?P(A)?Mutually exclusive(互斥事件）
Definition 2。4.1 Events A1,A2,AiAj??, ?i?j. n N,Anare called mutually exclusive, if Theorem 2。4.1 If A and B are mutually exclusive， then 概率论与数理统计英文版总结(word版可编辑修改) P(AB)?P(A)?P(B) (2。4。1) Mutually independent 事件的独立性
Two events A and B are said to be independent if
P(AB)?P(A)?P(B)
Or Two events A and B are independent if and only if
P(B|A)?P(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(B|A)?P(AB) if P(A)?0. （2。P(A)5。1） The multiplication theorem乘法定理 If A1,A2, P(A1A2,Ak are events, then Ak)?P(A1)?P(A2|A1)?P(A3|A1A2)P(Ak|A1A2Ak?1)
If the events A1,A2,{i1,i2,,im}?{1,2,,k},
,Ak are independent， then for any subset
P(Ai1Ai2A)?P(A)P(A)imi1i2P(A)
im(全概率公式 total probability）
Theorem 2.6.1。 If the events B1,B2,,Bk constitute a partition of the sample space S such that P(Bj)?0 for j?1,2,,k, than for any event A of S, P(A)??P(ABj)??P(Bj)P(ABj) (2。6。2） j?1j?1kk
概率论与数理统计英文版总结(K12教育文档)
