Two electronic components of a missile system work in harmony for the success of the total system.

Let X and Y denote the life in hours of the two components. The joint density of X and Y is f(x, y) = ye−y(1+x)

, x, y ≥ 0, 0, elsewhere.

(a) Give the marginal density functions for both random variables.

(b) What is the probability that the lives of both components will exceed 2 hours?