# Probability of x failing before y

tony3333
hi,
i have a problem and i really want you to help me with it.
if we have: density of X : f(x)=exp(-x), and density of Y : f(y)=2*exp(-2y) (independent components), what is the probability that X component fails first?
(it should be a number)
thank you

Staff Emeritus
Homework Helper
If I understand correctly, you will want P{X<Y}.

You can calculate this as follows: let $$A=\{(x,y)~\vert~0\leq x\leq y\}$$
Then you need to calculate

$$\int\int_A{2e^{-x}e^{-2y}dxdy}$$

tony3333
If I understand correctly, you will want P{X<Y}.

You can calculate this as follows: let $$A=\{(x,y)~\vert~0\leq x\leq y\}$$
Then you need to calculate

$$\int\int_A{2e^{-x}e^{-2y}dxdy}$$

$$\int_A{e^{-x}dx \int_A{2e^{-2y}dy$$