5

After the bus incident, Raye Penber asks Yagami Light to keep seeing him a secret from the police, Yagami agrees and says "I won't tell anyone, including my father". Wouldn't Raye Penber ask himself why would Yagami Light think I know his father is in the police force? Doesn't it give a hint that Yagami knows he's being investigated? Do we just accept that Raye Penbar is a dull FBI agent?

6

Light mentions that his father is a police detective when he passes a note to Yuri saying that he will try to subdue the bus hijacker:

Don't worry, Yuri. It'll be okay. I'm going to look for a chance to grab the guy's arm and pin him down so he can't use the gun. My dad's a detective and he's taught me what to do in emergencies like this. The guy's pretty small and weak-looking. I'm sure I can restrain him. [Translation from the fan Wikia.]

Since Raye Penber sees the note, it wouldn't be suspicious for Light to assume that Penber knows that he is the son of a police detective even if he never says so directly to him.

Note also that Light's actions suggest that he has more familiarity with what to do in these situations than the average person: beyond coming up with this "plan," he also asks Raye Penber to prove that he isn't an accomplice because it's "common to have someone hidden in the back to come help if anything goes wrong" for the hijacker. Thus, even if he didn't explicitly say that his father was a detective, it'd still be reasonable for someone to assume that he has some connection to law enforcement.

As an aside, Light's comment after Raye Penber proves his identity does seem slightly unnecessary:

Okay, I trust you, and I won't ask what an FBI agent is doing on a bus in Japan.

This indicates that he knows that Raye Penber is up to something, but then again, when he's already proved himself to be more suspicious and street-savvy than the average person, it's not that suspicious for him to say that. It's not like he's indicating that he knows that the FBI are there for the Kira investigation as opposed to something else.

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