Independent and identically distributed random variables 
,
..., 
are mutually independent
and have the same statistical distribution.
For random variables taking real
values, identical distribution means having a common distribution
function. Independence and identical distribution are separate requirements,
and neither one implies the other.
Independent and identically distributed observations are often abbreviated i.i.d. This assumption permits many sampling distributions and asymptotic results to depend on a single common population distribution.
