In its common form, the random variables must be identically distributed.

Note that, conditioned on the output distribution, the variables are independent identically distributed.

Among other things, the error terms are normally and identically distributed.

The variates do not have to be identically or symmetrically distributed.

Thus, the buyers' expected values are independently and identically distributed.

In the exposition above, it is assumed that the data are independent and identically distributed.

Secondly, error terms are assumed to be serially independent and identically distributed.

Assume that the processes followed by the m sites are Markovian independent, identically distributed and constant in time.

Such techniques usually require the sample to be independent and identically distributed which is not the case for a time series like security prices.

For identically distributed X this simplifies to the identity stated before.