The life span of a particular mechanical part is a random variable described by the following PDF:
If three such parts are put into service independently at t=0, determine a simle expression for the expected value of the time until the majority of the parts will have failed.
I can get the PDF: $$ f_L(l) = 0.4 (0 \leq l \leq 2) \\ f_L(l) = -0.4l + 1.2 (2 < l \leq 3) $$ and the expectation: $$ E(l) = \int_0^3 l f_L(l) dl \approx 1.27 $$
I think 'majority' means 2 or more, so we can focus on two parts of the three, and pay no attention to the third. The translation is $E(max(l1, l2))$, how will this be derived I currently have no idea.
Sorry about the misleading remark "$E(max(l_1, l_2))$", it's wrong to neglect the third part, because if that one fails early, then we only need one of the rest to fail.