The density function of the shorter lived life bulbs is f(x)=1/100 * e^{-x/100}.

The density function of the shorter lived life bulbs is f(x)=1/200 * e^{-x/200}.
The survival is 1 minus the integral of the density function. S(x)=e^{-x/100}, and
S(x)=e^{-x/200}.

The survival function for the entire group is (e^{-x/100})^{5} *
(e^{-x/200})^{5}.

The density function for the group is the derivitive of 1 minus the survival
function = e^{-3x/40}.

The mean for the group is the integral from 0 to infinity of x times the density function for the group = 40/3 hours.

Michael Shackleford, A.S.A.