Probability of x failing before y

  • Thread starter tony3333
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  • #1
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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
 

Answers and Replies

  • #2
22,089
3,296
If I understand correctly, you will want P{X<Y}.

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

[tex]\int\int_A{2e^{-x}e^{-2y}dxdy}[/tex]

this will be your probability...
 
  • #3
4
0
If I understand correctly, you will want P{X<Y}.

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

[tex]\int\int_A{2e^{-x}e^{-2y}dxdy}[/tex]

this will be your probability...

and because these are independent, we can separate the integrals and have

[tex]\int_A{e^{-x}dx \int_A{2e^{-2y}dy[/tex]

and then the variables of every probability , x,y, can be descibed by the same symbol, lets say t
but what should be the limits of the integral?
 
Last edited:

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