After a well known jewelry store was robbed in our town, police questioned the three most likely suspects: Bad Joe, Fast Gary, and Big Eric.

Here are the statements the three suspects gave to the police.

Bad Joe: "I didn't do it, and neither did Gary."
Fast Gary:"Joe didn't do it, Eric robbed the store."
Big Eric:" I have nothing to do with the robbery, Joe stole the jewelry."

Later, after the thorough investigation of this case, it was established that one of the suspects gave two false statements, one gave two true statements, and one gave one false and one true statement.

Who robbed the jewelry store?