“Peltzer's the name, Rand Peltzer.”|
—Rand introduces himself
Randall "Rand" Peltzer is the father of Billy Peltzer and the husband of Lynn Peltzer, as well as the one who originally bought the mogwai, whom he later names Gizmo, from Mr. Wing's store in Chinatown. Peltzer is a well-intentioned father who follows his dreams, despite that his inventions don’t always work.
Rand Peltzer is a struggling inventor who bought Gizmo from a Chinatown shop owned by Mr. Wing as a Christmas present for his son Billy, knowing only of the outward cuteness of the mogwai, and not understanding the true danger. As he leaves, Mr. Wing's Grandson tells Rand about the three rules he needs to know for taking care of a mogwai.
After the first rule is broken, and Gizmo quickly multiplies, he comes up with an idea to market the Mogwai as a new pet and even goes as far as to think that the mogwai might overtake the role of the most popular pet over the dog. Later another one of the three rules are forgotten and Gizmo multiplies while Rand is away at an inventors convention.
Later, as Randall with his family and Billy's girlfriend Kate Peltzer settle in the family home to enjoy the holidays until Mr Wing arrives. Mr Wing to Rand that he's not ready after learning of the Gremlin attack after taking Gizmo back with him, telling the family that one day he would allow Gizmo to return to Billy. As an apology for the Gremlin attack, Randall gives Mr. Wing a small token and a smokeless ash tray and Mr. Wing accepted it.
- He was supposed to get a cameo in Gremlins 2 and bring Billy a new rain-coat he invented to protect Gizmo from getting wet, but the scene was never filmed because the producers didn't think they needed it.