Death Penalty- Is it Right?

I do believe that in most cases death penalty is a deterrent to crime because if a person kills a whole bunch of people(on purpose) then they deserve to die because they will probably just end up doing it again. So for the public safety, serial killers and really horrible murderers can get the death penalty. When serial killers are killed they will never be out in public again, killing innocent people.
The biggest weakness is that if someone does receive capital punishment but they are innocent, the an innocent person just died for no reason! It's not fair if an innocent person dies in place of someone who is guilty and out in public still.
However, the biggest benefit of death penalty is that it would take serial killers and murders off of our streets forever. This is a big benefit because it makes the public feel safe and it is a great deterrent as well.
I cannot beleive that it costs so much money to keep a prisoner in jail for one year, and how much the death penalty is. It is a lot of money. I think that they should use death penalty when they really need to, and to incarcerate super serious crimes. And if possinble to use rehab more often because its less money and it is beneficial to the offender!