What are the random variables in Universal Hash Function? Universal hash function is defined as follow:

$f_{(k_0,k_1)}(x) = (k_0\cdot x + k_1) \mod p$, where $p$ is prime

In Wikipedia, it is mentioned that the above function is pairwise independent. Pairwise independence is defined here 

I wonder what are the random variables in $f$ and what pairwise independence means here.
The random variables are $k_0$ and $k_1$, typically taken to be uniformly distributed in $\mathbb Z/p\mathbb Z$ in this context.

(Sometimes we take $k_0$ to be uniform in $(\mathbb Z/p\mathbb Z)^\times$ instead, i.e. exclude $k_0 = 0$, but as long as $p \gg 2^{100}$ this is not important.)