# Some basic concepts of probability theory

xiaoxiao2021-04-11  401

1, random experiment

Features: All possible results can be listed by it. (In endless case, at least theoretically)

2, probability definition

Relative frequency definition: p (e1) = LIM (N1 / N)

P (e1) = 1, E1 is an inevitable event;

P (E0) = 0, E1 is an impossible event.

3, incompatible event: p (a or b) = p (a) p (b) (Note: "a or b" means A occurrence or B occurs)

Index: p (a and b) = p (a) p (b) (Note: "A and B" means A occurrence, B also happens)

4, Bayesian theorem

(On school)

Time to listen

The teacher said, did not understand, this time it is readily understood)

The Bayesian method is actually a deductive method (by general to special, also known as the Holmes law). It is known for a system event B, and ask for a certain reason event AK's probability. For example, the Titanic is known to sink, and the probability of imposing the problem of instrument.

An event B causes the reason for event B as a series of incompatible events {A1, A2, ..., AK, ...} = a. The probability of each cause event (P (AK)) is known, the reason for the difference (P (B | AK)) is known, then in the case of B, the probability caused by one reason (P (AK | B))

5, two distributions

One of two possible items per experiment.

6, probability density

7, accumulate distribution functions

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