How did prince's dad die in the movie purple rain?

The Kid (Prince) comes home to find his battered mother crying.

He enters the house, and find it disheveled and dark.

We then see his father standing against a wall, shakey, with a gun in his hand.

The kid turns on the light, and we hear a gunshot.

The next scene is the ambulance arriving. The Kid's dad is laying on the basement floor, still alive (but barely), suffering from having shot himself in the head.

He dies a while later.

Actually at the end of the movie, the Kid visits his dad at HCMC (hospital) So if he died or not is unknown. But in the sequel to Purple Rain, Graffiti Bridge, The Kid writes letters to his father in hopes that he will return one. So in the end I am assuming that he is alive.