please make sure the answer is a correct DFA!

4. (4 points) Convert the NFA defined by (q0,a)={q0,q1}.(q1,b)={q1,q2}(q2,a)={q2}(q0,)={q1,q2} with initial state q0 and final state q2 into an equivalent DFA. Assume the input alphabets are {a,b}