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0-1 distribution

Binomial distribution with n=1
synonym Bernoulli distribution (Discrete probability distribution) generally refers to 0-1 distribution
The 0-1 distribution is the case of n=1 Binomial distribution That is, only one event test will be conducted first, and the probability of the event occurring is p, and the probability of not occurring is 1-p. This is the simplest distribution, and there are only two results for any one Random phenomenon Both obey the 0-1 distribution.
Chinese name
0-1 distribution
Foreign name
0-1 distribution
Alias
Two-point distribution
Field
Probability Theory and Mathematical Statistics
Notation
X~B(x,p)
Application
statistics

definition

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set up Discrete random variable The distribution law of is
, where k=0,1. If p is the probability when k=1 (0<p<1), then X follows the 0-1 distribution, and the 0-1 distribution is also called the two-point distribution, which is recorded as: X~B (x, p)
Another mathematically related distribution is: Bernoulli Test( Binomial distribution ) [1]
If Random test E meets: repeat a test for n times under the same conditions, and each test has only two results A and
, of Event A probability Keep unchanged in each test, P (A)=p, P(
)=1-p; The results of each test are different from each other influence , then Random test E is n times Bernoulli Test.

Distribution law

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A random event X, the occurrence of X is recorded as X=1, and the non occurrence of X is recorded as X=0. If event X obeys the 0-1 distribution, then the distribution law of X is:
X
zero
one
p x
1-p
p

nature

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Variance: D (X)=p (1-p)

give an example

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That is, only one event test is conducted first, and the probability of the event is p, and the probability of not happening is q=1-p. This is the simplest distribution, and there are only two results for any one Random phenomenon For example, flip a coin to observe the front and back, whether the newborn is male or female, and check whether the product is qualified. [2]