Why can't a convicted felon serve in the military?

also,have convicted felons ever served in the us military? And if they did were there any reports of criminal acts by these ex-felons and again if so what was crimes committed by ex-felons in the military higher or lower than crimes committed by people without felony convictions in the military? Im trying to see if there was statistical justification for the blanket prohibition or if it was just a decision based on preconceived notion?