How many random murders are there in the us each year?

In 2011, 1,481 homicides were committed where the victim/offender had no prior relationship (stranger killing strangers). However, 5,588 are "unknown" as to any type of victim/offender relationship.

The data is available at the link below

http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/expanded-homicide-data-table-10