Yepp this was also my thought but I read the following: Let [tex] f(t) [/tex] be an function, no properties listed but I guess that [tex] \int \limits_0^\infty f(t) dt < \infty [/tex] then they define:

[tex] mean = \frac{\int \limits_0^\infty t f(t) dt}{\int \limits_0^\infty f(t) dt} [/tex]

[tex] var = \frac{\int \limits_0^\infty (t-mean)^2 f(t) dt}{\int \limits_0^\infty f(t) dt} [/tex]