Well plenty of people got shot crossing the wall, but that's not really a "random shooting". Certainly much less random than "walking while black" or something.
Apparently there were 139 wall-victims in 29 years, so less than 5 per year, or about 0.03 deaths per 100k people per year. Apparently, twice as many people died of natural causes while crossing the border.
The US seems to have about 1000 shootings by police per year [2], which would be about 0.3 deaths per 100k people per year.
So the US has 10x more police-shootings than the GDR had wall-deaths per person.
[1] https://de.wikipedia.org/wiki/Todesopfer_an_der_Berliner_Mau...
[2] https://www.washingtonpost.com/graphics/national/police-shoo...