Answer 6!
In Act 1, scene 5 the ghost tells Hamlet he was murdered by his uncle Claudius. This signifies as the first time Hamlet wants revenge. The Ghost also tells Hamlet to not lose his head while trying to get revenge. He also wants Hamlet to leave his mother out of the situation. This seems like a pretty natural thing for a father to ask his son to do, the keep your head on straight part. So this leads us to believe the ghost really is Hamlet's father.