Let the times to breakdown for the processors of a parallel processing machine have joint density

\[f(x, y)= \begin{cases}0.04 e^{-0.2 x-0.2 y} & \text { for } x>0, y>0 \\ 0 & \text { elsewhere }\end{cases}\]

where \(x\) is the time for the first processor and \(y\) is the time for the second. Find

(a) the marginal distributions and their means;

(b) the expected value of the random variable whose values are given by \(g(x, y)=x+y\).

(c) Verify in this example that the mean of a sum is the sum of the means.