Sequence of identical experiments, each outcome one of *r* possible
ones, with probabilities
.
Denote by *X*_{i} the number of the outcomes that result in *i*.
The joint distribution of
is
the multinomial, the *X*_{i}'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: