Independent Identically Distributed

A sequence E1,…,EnE_1,\dots,E_n of Random Variables is iid iff they are independent

P(Ej∣E(j−1),E(j−2),…)=P(Ej)\mathrm{P}\left(E_j \mid E_{(j-1)}, E_{(j-2)}, \ldots\right)=\mathrm{P}\left(E_j\right)

and identically distributed

P(Ei)=P(Ej).\mathrm{P}\left(E_i\right)=\mathrm{P}\left(E_j\right).

For example a sequence of die tosses is iid.