A random sampleof a random variableXis such that

The random variables representing the sample values (before the sample is taken) are all statistically independent and identically distributed.

The random variables representing the sample values (before the sample is taken) are all statistically independent but need not be all identically distributed.

The random variables representing the sample values (before the sample is taken) are all identically distributed but need not be all statistically independent.

The random variables representing the sample values (before the sample is taken) can be non-identically distributed and statistically dependent.