I do not understand why Dmitri originally doubted that Smerdyakov murdered Fyodor but later changed his mind and thought Smerdyakov murdered Fyodor.
Be sure to go into www.sparknotes.com/lit and find this book under the B's -- then read the section called Analysis of Major Characters. Dmitri is at the bottom, but be sure to read about the others, too, so you understand the references made about Dmitri's character.
Please be sure to re-post if you need further help.
=)