A jury has been picked for the federal corruption trial of the former speaker of the Massachusetts House of Representatives. Salvatore DiMasi and two others are charged in a scheme to rig lucrative state contracts for the software company Cognos in exchange for payments. Jury selection was completed Tuesday. Eight men and eight women were chosen to hear the case, including four alternate jurors. Opening statements are expected Thursday. DiMasi and co-defendants Joseph McDonough and Richard Vitale have pleaded not guilty. A fourth man charged in the scheme, Joseph Lally, cut a deal with prosecutors and is expected to testify against the others. The list of potential witnesses includes Gov. Deval Patrick, Senate President Therese Murray and DiMasi’s successor, House Speaker Robert DeLeo.