Anyone can believe in God. Christians, of course, believe in God. Pseudo-Christians believe in God. Various religions, while they would strongly disagree with who God is, believe in God. Even atheists sometimes believe in God, they just don't want to. And of course, Satan, who has had the privilege of actually having met God, believes in God.
Of all those groups, only one has the kind of faith that actually saves. Faith is more than just intellectual assent. Faith is the substance of things hoped for (Hebrews 11:1). If you have faith in God, you don't just believe He exists, you hope He will fulfil His promises.
If you hope for something, it's logical to act in accordance with that. If I say "I hope I get this grade on my assignment", it makes no sense for me to just set the assignment aside until the deadline, handing in a blank sheet of paper at the end. What should I do? I should work towards getting the assignment done, and to the satisfaction of my teacher.
As a Christian, I have hope in God. I never saw the resurrection, nor have I seen Heaven, but I hope that I have been forgiven for my sins, and will inherit eternal life. Unlike schoolwork, you can't fail with Christ, but if you truly hope for such a thing, doesn't it make sense to act like it? "I hope I'm going to Heaven!" Ok, then live like a citizen of Heaven! "I hope I won't go to Hell", then stop acting like a child of Hell. If you have true faith in Christ, your actions should reflect that.