1 and y2 denote the lengths of life, in hundreds of hours, for components of types i and ii, respectively, in an electronic system. the joint density of y1 and y2 is given by f(y1, y2) is
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}(1 / 8) y_{1} e^{-\left(y_{1}+y_{2}\right) / 2}, & y_{1}>0, y_{2}>0, \0, & \text { elsewhere. }\end{array}\right.\)
One way to measure the relative efficiency of the two components is to compute the ratio . Find . [Hint: In Exercise 5.61, we proved that and are independent.]