Depends on the area. I know of people from black, white and asian backgrounds who've been attacked by people of the same or different races. In my experience, its not so much about race but about looking 'weak' or simply being a random target for someone on drugs or in a gang. Not sure about cops not investigating for reasons you've put forward but most of the crimes I know about (concerning me, friends or family members from all different backgrounds)- esp muggings- go unsolved just because the cops have other priorities or lack of funding (I'm assuming here).