Law of large numbers, central limit theorem and some common distribution

Such record something does not make sense , look at the origin, application, and more with thinking have value

First, the law of large numbers

(1) law of small numbers:

  • If statistics rarely, then the event on the performance of a variety of extreme conditions
  • And these cases are accidental event
  • He is saying nothing to do with expectations

(2) law of large numbers:

  • If the data is large enough, then the probability of events occurring more close to its expected value

 

Second, the central limit theorem

  Given a general any distribution, every I n th random samples from the population, a total of m times pumping. This sample group were then m average value, the average value is too distributed approximately obey

 

Third, the common distribution

1, evenly distributed

X sample probability interval falls within a ~ b are the same. The probability density for x

 

2, Bernoulli distribution

The results of the sample only two. For example coin toss, either 0 or 1.

 

3, binomial distribution

Do Bernoulli experiment n times, each time the results of only 0,1. If n = 1, then obviously Bernoulli distribution

 

4, Poisson distribution

Suppose we mean the number of known samples appear as λ, the number of occurrences of the sample within a certain period of time, the probability distribution of this sample is also called the Poisson distribution, which belongs to the discrete distribution.

 

5, exponential distribution

If desired sample occurring within a predetermined time known λ, then its probability distribution at time t of exponential

  

  • Poisson statistics the number belongs to happen
  • Statistics exponential distribution has occurred 

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Origin www.cnblogs.com/ylxn/p/11877509.html