Q5 An electronic device consists of two components. Let
x
and
Y
[years] be the times to failure of the first and second components, respectively. Assume that
(x,Y)
has the density
f(x,y)=4e^(-2(x+y))
if
x,y
both are
>0
and 0 otherwise. (a) Are
x
and
Y
dependent or independent? (b) Find the densities of the marginal distributions. (c) What is the probability that the first component will have a lifetime of 2 years or longer?