From the October GQ, an interview with Dr. Dre:

I read that you didn’t want to put “Fuck tha Police” on the first record, but an experience changed your mind.

Nah, that’s not true. The experience motivated the song.

Can you tell me what it was?

It was me and Eazy riding around. He had this paintball gun, and he was shooting people at bus stops. The cops caught us and we were facedown on the freeway, with guns pointing at us,. We thought it was bullshit. So we want to the studio and created the song.

I’m going to write a new song. It’s gonna be called “Fuck tha Chucklehead Who Shot my Mom at a Bus Stop with a Paintball Gun.” It’s going to be an underground classic that encapsulates a poetic new strain of streetwise reality. And the cool thing is that only a select group of people will really be able to appreciate its gritty potency. One of their characteristics will be knowing the demographics of the typical LA bus rider.