The random variables $X_1,\ldots,X_n$ are called a random sample of size $n$ from the population $f(x)$ if $X_1,\ldots,X_n$ are mutually independent random variables and the marginal pdf of pmf of each $X_i$ is the same function $f(x).$ Alternatively, $X_1,\ldots,X_n$ are called independent and identically distributed random variables with pdf or pmf $f(x).$ This is commonly abbreviated to iid random variables.