Hi I am having some trouble with this statistics question. Y1 and Y2 denoted the lengths of life, in hundreds of hours, for components of types I and II, respectively, in an electronic system. The...

Hi I am having some trouble with this statistics question.

Y1 and Y2 denoted 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
f (y1, y2) =((1/8)*y1*e ^(−(y1 +y2)/2) where y1 > 0, y2 > 0,

- and the function is 0 elsewhere

The cost C of replacing the two components depends upon their length of life at failure and is given by C = 50 + 2Y1 + 4Y2. Find E(C) and V (C).

I undrestand that this is an exponential distribution. Do we use an mgf table to find the alpha and beta or is there a better way to compute the E(C) and V(C).