EAST LANSING, Mich., Feb 14 (Reuters) - Authorities on Tuesday said they have "no idea why" a 43-year-old gunman killed three Michigan State University students and wounded five in the latest U.S. mass shooting, but said he had a history of mental health problems before the shooting spree that ended with him turning the gun on himself.

The gunman, identified as Anthony Dwayne McRae of Lansing, Michigan, shot himself to death after the rampage on Monday night, Jim Tarasca, special agent in charge of the FBI's Detroit office, said at a briefing. McRae had no known affiliation to the university in East Lansing, about 90 miles (145 km) northwest of Detroit.y