This is really just another variation of the nearly universal "Engineer" humor theme. For another one (shorter, but almost identical in theme) see "Engineers".
These three Texans go down to Mexico one night, get drunk, and wake up in jail only to find out that they are to be executed in the morning, though none of them can remember what they did the night before.
The first one is strapped in the electric chair and is asked if he has any last words. He says, "I am from the Baylor school of divinity and I believe in the almighty power of God to intervene on behalf of the innocent. "They throw the switch and nothing happens, so they figure God must not want this guy to die and they let him go.
The second one is strapped in and gives his last words, "I am from the University of Texas School of Law and I believe in the power of justice to intervene on the part of the innocent." They throw the switch and again nothing happens. They figure that the law is on this guy's side, so they let him go too.
The last one is strapped in and says, "Well, I'm a Texas Aggie Electrical Engineer, and I'll tell you right now you ain't gonna electrocute nobody if you don't connect them two wires."