A scene from Hot Shots starring Charlie Sheen:
Comment: I believe the Indian yells "Me-e-e!" as he jumps.
This scene presents the stereotype and invites you to laugh at it. Unfortunately, it's not particularly funny.
As I noted in Why Jumpers Yell "Geronimo," jumping from a plane is supposedly a death-defying act of bravery. Thus we associate it with Geronimo, who's our emblem of raw, maniacal, semi-suicidal courage.
Of course, the Indian in the scene looks like a generic "brave," not Geronimo. But to viewers, all Indians are the same. They're all half-crazed savages who will attack a wagon train, torch a cabin of "innocent" settlers, or leap to their death with equal abandon.
For more on the subject, see Obama: Bin Laden Was "Geronimo" and Alternatives to "Geronimo" Codename.