Steven Tyler -- Drops F-Bomb on 'Today' Show

Steven Tyler had a rough morning -- not only did he not know what show he was on, he also dropped an F-bomb on live television!

Tyler -- who is probably never awake at such an early hour -- performed with Aerosmith on the "Today" show this morning ... only he thought he was on a different program. Al Roker's reaction ... priceless.

Then, while Roker was giving a weather update, Tyler screamed in the background to the crowd, "Thanks for coming out, you crazy f**ks!"