An electronic device consists of two components. Let X and Y be the length of time until failure (in years) of the first and second component, respectively. Assume that (X;Y) has the probability density function f(x,y) = k(x*y^2 + 2*y*x^2) if 0 <= x <= 6 and 0 <= y <=8 and 0 otherwise.
(a) Find the marginal density functions f1(x) and f2(y).
(b) Are X and Y dependent or independent?
(c) Find the expected lifetimes of the two components.
(d) What is the probability that the device will last longer than three years?
(e) What is the covariance of the component lifetimes of the device?