  We compute the tail asymptotics of the product of a beta random variable and
a generalized gamma random variable which are independent and have general
parameters. A special case of these asymptotics were proved and used in a
recent work of Bubeck, Mossel, and R\'acz in order to determine the tail
asymptotics of the maximum degree of the preferential attachment tree. The
proof presented here is simpler and highlights why these asymptotics hold.
