It's been years (decades?) since I've seen the I, Claudius miniseries and even longer since I've read Robert Graves' books. It's therefore entirely possible that this scene was in one or the other or both, but if so I had forgotten it.
In his biography of the emperor Caligula, Robert A. Barrett relates the untimely death of Claudius' son, Claudius Drusus. In about AD 20, the boy (who could have been no more than about 11 at the time, his mother having married Claudius in about AD 9) became engaged to Junilla, the daughter of the then-rising praetorian prefect Sejanus (she was about four years of age).
It was a short-lived union. A few days later the boy, perhaps anxious to prove that he had not inherited his father's clumsiness, threw a pear into the air, deftly caught it in his mouth, then choked to death.
[Claudius] had children by three of his wives: by Urgulanilla, Drusus and Claudia; by Paetina, Antonia; by Messalina, Octavia and a son, at first called Germanicus and later Britannicus. He lost Drusus just before he came to manhood, for he was strangled by a pear which he had thrown into the air in play and caught in his open mouth. A few days before this he had betrothed him to the daughter of Sejanus, which makes me wonder all the more that some say that Drusus was treacherously slain by Sejanus.