Should death penalty be legalized?

Capital punishment, or the Death Penalty is the sentence given by a judge, or a state, to a criminal.
It is still legal in some states, through electrocution, hanging, lethal injection, gas chamber, and firing squad.(being shot in public)
On some special circumstances, I do somehow agree that death penalty should be legalized.But as I said, only on some cases.

*Pros*
1.It is less expensive to kill a man rather than holding him in prison for life, giving him food and cover.
2.The people would be more scared to commit crimes now that they know that this could cause their deaths.
3.People from sanatoriums, mentally ill, would suffer less.
4.As a prisoneer sentenced to prison for life, you could escape and murder more people.
5.It contribues to the overpopulation issues.
6.Victims' families would feel better about the murder dying.

*Cons*
1.The murders' families would suffer more.
2.It is more barbaric rather than putting the murderer in prison.
3.The possibility exists that innocent men and women may be put to death.

Mainly, this are the most important Pros and Cons.I do think that Death Penalty should be lagalized, because (read the pros).