Exactly who is related to whom in the Marsh family is never consistent. Early episodes imply that Jimbo and Marvin (Stan's grandfather) are on Sharon's side of the family, whereas more recent ones imply they are on Randy's side. Being on Sharon's side makes sense for Jimbo, as he has a different last name. However, Marvin's last name is, indeed, confirmed to be Marsh. Matt Stone revealed in an interview that Jimbo Kerns is Randy's half-brother.