About a month ago, Martin Shkreli, the pharmaceutical entrepreneur who was arrested on Thursday, began live-streaming himself on YouTube, sometimes for 10 hours or more at a time, as he worked, played video games, strummed a guitar and, occasionally, while he slept.

He would also chat with his audience, defending himself to critics upset about accusations of drug price gouging and seeming to taunt fans of Wu-Tang Clan asking him to play the sole copy of the group’s latest album, which he reportedly purchased at auction. (So far, he had yet to play the music on the stream.)

The live streams are preserved on his YouTube account. There are boring moments (Mr. Shkreli sleeping) and some odder ones, such as Mr. Shkreli debating drug prices and politics with a group of students apparently from his alma mater, Hunter College High School in New York.

That exchange, on Monday, began when a girl who identified herself as a senior at Hunter connected with him via Skype.