概率论与数理统计公式Word文档下载推荐.docx

1、（5） basic events, sample spaces and events in a test, regardless of the number of events, can always find such a group of events, it has the following properties:Each trial must occur and only one event in this group occurs;Any event is made up of some of the events in this group.Each event in such

2、a group of events is called a basic event, which is used to represent the event.The whole of the basic event is called the sample space of the test.An event is a collection of parts （basic events） in it. Capital letters A, B, C are usually used,. Representing events, they are subsets.Is it an inevit

3、able event, an impossible one?.The probability of an impossible event is zero, and the event with zero probability is not necessarily an impossible event; similarly, the probability of the inevitable event （omega） is 1, and the event with probability 1 is not necessarily an inevitable event.（6） the

4、relationship between events and operations:If the component of the event A is also a part of the event B, （A happens, there must be an event B）:If there is a simultaneous event, the event A is equivalent to the event B, or A equals B:A=B.There is at least one event in A and B: A B, or A+B.An event t

5、hat is part of A rather than B is called the difference between A and B, denoted as A-B, and can also be denoted as A-AB, or it represents the event that B does not happen when A occurs.A and B occur simultaneously: A, B, or AB. A B=?, which means that A and B cannot happen at the same time, called

6、event A incompatible with event B or mutually exclusive. Basic events are incompatible.-A is called the inverse event of event A, or the opposite event of A. It represents an event that does not occur in A. Mutual exclusion is not necessarily opposite.Operations:Binding rate: A （BC） = （AB） C, A （B,

7、C） = （A, B）, CThe distribution rate （AB）, C= （A, C） a （B, C） （A, B） C= （AC）, （BC）The rate of probability: （7） the axiomatic definition of probability is set as a sample space. For events, there is a real number P （A） for each event, if the following three conditions are satisfied:1 0 = P （A = 1）,2 d

8、egree P （omega） =13 degrees for 22 incompatible events,. YesIt is often called countable （complete） additivity.P （A） is called the probability of events.（8） the classical probability model is 1 degrees,2 degree.Set any event, it is made up of, there isP （A） = =（9） geometric probability if the random

9、 test results for infinite uncountable and each results the possibility of uniform, and every basic event in the sample space can be used to describe a bounded region, said the test for random geometric probability. A for any event,. L is geometric measure （length, area, volume）. （10） additive formu

10、la P （A+B） =P （A） +P （B） -P （AB）When P （AB） = 0, P （A+B） =P （A） +P （B）（11） subtraction formula P （A-B） =P （A） -P （AB）When B A, P （A-B） =P （A） -P （B）When A=, P （） =1- P （B） （12） conditional probability defines A and B are two events, and P （A） 0 is called the conditional probability of event B occurr

11、ing in event A.Conditional probability is a kind of probability, and all probability properties are suitable for conditional probability.For example, P （omega /B） =1 P （/A） =1-P （B/A） （13） multiplication formula multiplication formula:More generally, for event A1, A2,. An, if P （A1A2. An-1） 0, but t

12、here is 。（14） independence: the independence of the two eventsEvent and satisfaction are called events, and they are independent of each other.If events are mutually independent, and then there areIf events are independent of each other, they can be separated from each other.Inevitable events and im

13、possible events are independent of any event.Is mutually exclusive to any event.The independence of multiple eventsLet ABC be three events, if 22 independent conditions are satisfied,P （AB） =P （A） P （B）; P （BC） =P （B） P （C）; P （CA） =P （C） P （A）And satisfy P （ABC） =P （A） P （B） P （C） at the same timeS

14、o A, B, C are independent of each other.Similar to n events.（15） all probability formula sets event satisfaction1 degrees 22 incompatible each other,2 degree,Is there（16） Bias formula set event,. And satisfaction1 degree,. 22 incompatible, 0, 1, 2,. ， ，2 degree,beI=1, 2,. N.This formula is the Bayes

15、 formula.（,. A priori probability. （,. It is usually called posterior probability. The Bias formula reflects the causal probability law, and made by Shuoyin fruit inference.（17） we have done a test on Bernoullis hypothesisEach trial has only two possible outcomes that occur or do not occur;The secon

16、dary test is repeated, i.e., the probability of occurrence is homogeneous at each time;Each trial is independent, that is, whether each trial occurs or not does not affect the occurrence of other trials.This experiment is called the Bernoulli model, or the heavy Bernoulli test.The probability of occ

17、urrence of each trial is expressed as the probability of the occurrence of the second in the heavy Bernoulli test,， 。The second chapter random variable and its distribution（1） the probability of discrete random variable is Xk （k=1,2）,. And take the probability of each value, that is, the probability

18、 of the event （X=Xk） isP （X=xk） =pk, k=1,2,. ,The upper bound is the probability distribution or distribution law of discrete random variables. It is sometimes given in the form of distributed columns:Obviously, the distribution law should meet the following conditions:（1）, （2）.（2） the distribution

19、density of continuous random variables is the distribution function of random variables. If there is a nonnegative function, there is an arbitrary real number,It is called continuous random variable. Probability density function or density function, referred to as probability density.The density fun

20、ction has the following 4 properties:1 degree.（3） the relationship between discrete and continuous random variablesThe function of the integral element in the theory of continuous random variable is similar to that in the theory of discrete random variables.（4） the distribution function is a random

21、variable, and it is an arbitrary real numberThe distribution function of X, a random variable, is essentially a cumulative function.You can get the probability that X falls into the range. The distribution function represents the probability of the random variable falling into the interval （-, x）.Th

22、e distribution function has the following properties:1 degree;2 degrees are monotone decreasing functions;3 degree,;4 degrees, that is, right continuous;5 degree.For discrete random variables,;For continuous random variables,. （5） eight distribution, 0-1 distribution P （X=1） =p, P （X=0） =qIn the Nou

23、ri test, the two distribution is the probability of event occurrence. The number of events is a random variable, and if it is, it may be valued as.Among them,It is called the two distribution of random variables obeying the parameter. Remember as.At that time, this is （0-1） distribution, so （0-1） th

24、e distribution is a special case of the two distribution.The distribution law of random variables is given by Poisson distribution， ， ，The Poisson distribution, which is called the random parameter, is denoted as or P （）.The Poisson distribution is the limit distribution of the two terms （np=, N, P）

25、.Hypergeometric distributionThe hypergeometric distribution of the random variable X follows the parameter n, N, M, denoted by H （n, N, M）.The geometric distribution, wherein P = 0, q=1-p.The geometric distribution of the random variable X obeying the parameter p is denoted as G （P）.The value of the

26、 random variable is only a, b, and the density function is constant on a and bOther，The random variable is uniformly distributed on a and b, and is denoted as XU （a, B）.The distribution function isWhen a = x1x2 = B, X falls in the range of （） in probability. exponential distributionAmong them, the e

27、xponential distribution of the random variable X obeys the parameter.The distribution function of X isRemember the integral formula:The density function of random variables is normal distribution， ，Where the constant is called the random variable, the normal distribution or Gauss （Gauss） distribution is assumed as the parameter.It has the following properties:The figure of 1 degrees is about symmetry;At 2 degrees, the maximum value was then;If, then the distribution function is.The normal distribution of parameters and time is called the normal nor