Is my regular expression and finite automata diagram for this state table correct? So i have some theory of computer science homework and I'm struggling with this question currently. I am given the following automaton:

$Q = \{q_0,q_1\}$.
$\Sigma = \{a,b\}$.
$q_0 = q_0$.
$F = \{q_0\}$.
$\delta(q_0,a) = \delta(q_0,b) = q_1$, $\delta(q_1,a) = \delta(q_1,b) = q_0$.

I have to do two things: draw a state diagram, and write an equivalent regular expression. For now, these are my answers. I think my diagram is correct, but I'm not sure about the regular expression.

My regular expression for now is $(a+b)^*(a+b)$. Any help is very much appreciated.
Your automaton accepts all words of even length, whereas your regular expression accepts all words of positive length. The most common way to express the language of all words of even length as a regular expression is $(\Sigma\Sigma)^*$, where $\Sigma$ is a common shortcut for an arbitrary letter of the alphabet (in your case, $\Sigma$ stands for $a+b$).