What are the random variables in Universal Hash Function?
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.)