Definition indepedence and identically distributed (iid)

Question

Bruce Hansen's book "Econometrics" defines a random sample as follows: "The observations $(y_i,x_i, z_i)$ are a random sample if they are mutually independent and identically distributed $(iid)$ across $i =1, ..., n.$"

I have two questions about this definition: $1)$ Can two observations be iid or does the concept of iid apply only to random variables? In other words, each observation must be associated with a random variable. And the different observations correspond to the result of the same experiment. $2)$ Since each observation is made up of three elements $(y_i, x_i, z_i)$, then should each observation be considered as the realization of a random vector? So the concept of iid refers here to the independence and identical distribution of random vectors and not random variables?

Answer 1

Both independence and having a distribution are properties that can be possessed only by random variables. In your example $y_i, x_i,z_i$ is a random vector, where for each $i$ they jointly have identical distribution and are independent of other such triplets. What we mean by such definition is that we treat the observations as realizations of the random variables.