A particular model of an HDTV is manufactured in three different plants, say, A, B, and C, of the same company. Because the workers at A, B, and C are not equally experienced, the quality of the units differs from plant to plant. The pdf's of the time-to-failure X _A , X _R , X _c , in years, are

Plant A produces three times as many units as B, which produces twice as many as C. The TVs are all sent to a central warehouse, intermingled, and shipped to retail stores all around the country. What is the expected lifetime of a unit purchased at random?

fx (1)= 5 1 1. exp 0, - exp 0, fx (x)={6.5' x. (x)= 1% xp 0, X 6.5 10 x>0, 0, W. x > 0, 0,W. x>0, for A 0,W, for B for C,