Probability
Axiomatic definition
Definition of requirements for the probability of any single probability must meet the following conditions:
Non-negative:
Normative:
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Countable additivity:
For countable pairwise mutually exclusive events (natural number), there is
I.e. either event probability must be greater than or equal to 0 and less than or equal to 1;
Probability sample space is 1;
And the probability of mutually exclusive events is equal to the probability of mutually exclusive events and.
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Arrangement formula
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Combination formula
Subjective probability
Subjective probability can be understood as a state of mind or tendencies, it is not built on a solid basis, and therefore people recognized.
The classical definition
There is provided a test equally likely outcomes, and the event happens to include results of them, then the probability of an event is defined as:
Statistical definition
Statistical definition of ideology: a large number of repeat test, the frequency of events, to estimate the probability of the event.
Hypotheses tests, in which the event occurred times, then the probability of an event can be equal to the frequency of their occurrence, namely
Conditional Probability
definition
At an event B occurs, the probability of an event A occurs is called the conditional probability, written as:
Independent events
Independent means or not is not affected by the occurrence of an event of other events. Generally used to define the conditional probability:
I.e. equal to the probability of occurrence of A and A occur under condition B occurs , then said independent B. A
Bayesian formula
According to the conditional probability formula
Have
There are similar
Simultaneous availability:
Reproduced in: https: //www.jianshu.com/p/e10d4ca461f1