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Math Help - Probability P(X<Y<Z)

  1. #1
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    Probability P(X<Y<Z)

    I'm wondering about the following problem: Let $f_{X,Y,Z}(x,y,z)=e^{-(x+y+z)}$ for x,y,z>0. Find $P(X<Y<Z)$. I've seen the solution to this at http://www-rohan.sdsu.edu/~babailey/.../lecture10.pdf, but I don't understand how they went from P(X<Y<Z) to the triple integral. How does one work with an expression as P(X<Y<Z)? Thanks.
    Last edited by MagisterMan; June 23rd 2013 at 06:16 AM.
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  2. #2
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    Re: Probability P(X<Y<Z)

    Quote Originally Posted by MagisterMan View Post
    I'm wondering about the following problem: Let f_{X,Y,Z}(x,y,z)=e^{-(x+y+z)} for x,y,z>0. Find $P(X<Y<Z)$. but I don't understand how they went from P(X<Y<Z) to the triple integral. How does one work with an expression as P(X<Y<Z)
    P(X<Y<Z) mean what it says: points \{(x,y,z) : 0<x<y<z\} so the integrals are \int_o^\infty  {\int_0^z {\int_0^y f } } dxdydz
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    Re: Probability P(X<Y<Z)

    Thanks. I think I need to brush up on my multivariable calculus...
    Last edited by MagisterMan; June 23rd 2013 at 01:01 PM.
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