Probability of x failing before y

[tony3333]

Homework Statement

hi,
i have a problem and i really want you to help me with it.
we have X and Y that fail independently of each other.
density of X : f(x)=exp(-x), and density of Y : f(y)=2*exp(-2y) what is the probability that X component fails first?
(it should be a number)
thank you

 

[hgfalling]

You need to show some work. What have you tried?

 

[tony3333]

so, i think, i need the probability of X failing and Y not, at a time T.
T T T oo
so it is Pr=∫f(x)dx *(1-∫f(y)dy)=∫2*exp(-2t)dt * ∫2*exp(-2t)dt=
0 0 0 T
and here i am stuck...


(the limits of the first integral are (0,T), second (0,T), third (0,T), and forth (T, +oo)