random sample

A random sample is a set of random variables that are independent and identically distributed.

Formally,
a set $\{X_1,X_2,\dots ,X_n\}$ is a random sample of size $n$ if

• the random variables $X_1,X_2,\dots ,X_n$ are mutually independent
• the random variables $X_1,X_2,\dots ,X_n$ share the same probability distribution

and we say $X_1,X_2,\dots ,X_n$ are i.i.d., i.e. independent and identically distributed.