Basic terminology question.
I hear “let the sample be i.i.d.“ and “let these random variables be i.i.d.” being used interchangeably.
Even Wikipedia uses both:
A collection of random variables is independent and identically distributed if...
It is commonly assumed that observations in a sample are effectively i.i.d.
Are there different nuances or are they equivalent?
Also, are the points in a sample regarded as repeated measurements of one random variable, or one measurement each of multiple i.i.d. random variables?