Sequence of identical experiments, each outcome one of r possible ones, with probabilities . Denote by Xi the number of the outcomes that result in i. The joint distribution of is the multinomial, the Xi's are not indpendent.
Mutually Independent events:
The events are said to be mutually independent iff for every subset of events , we have the multiplicative property of intersection:
Mutually Independent random variables:
The random variables are said to be mutually independent iff for any vector in the cartesian product state space , we have: