Necessary conditions. E(XY)=E(X)E(Y) can be derived from the independence of X and Y, but E(XY)=E(X)E(Y) cannot be derived from the independence of X and Y, only X and Y are irrelevant (covariance is 0).

Definition: Let A and B be two events. If the equation P(A∩B)=P(AB)=P(A)P(B) is satisfied, events A and B are said to be independent of each other.

1, P(A∩B) is P(AB).

2. if p (a) >; 0, P(B)>0, the independence of A and B and the incompatibility of A and B cannot be established at the same time, that is, independence must be compatible and mutual exclusion must be related.

Extended data

Promotion:

Let A, B and C be three events, if P(AB)=P(A)P(B), P(BC)=P(B)P(C), P(AC)=P(A)P(C), P(A, B, C) = P (A).

A more general definition is A 1, A2, ..., an is n(n≥2) events. If any two, any three, ... and any n events are equal to the product of the probability of each event, then events A 1, A2, ..., and are independent of each other.

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