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Math Help - joint prob density?

  1. #1
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    joint prob density?

    in ref to earlier thread http://www.mathhelpforum.com/math-he...tml?pagenumber=

    I have stumbled upon a question which poses an identical problem but not in the form of an exam question therefore i suppose you could sketch it although from the simplicity of it i doubt this is really necessary.

    If someone could show how they obtained this answer,,,and then give a valid proof to a valid method for my previous thread i'd appreciate the help,,

    Q: Random variables x and y have jonint density function exp(-x-y) x.y>o

    findp(x>y) answer back of book is 1/2
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by bluesblues View Post
    in ref to earlier thread http://www.mathhelpforum.com/math-he...tml?pagenumber=

    I have stumbled upon a question which poses an identical problem but not in the form of an exam question therefore i suppose you could sketch it although from the simplicity of it i doubt this is really necessary.

    If someone could show how they obtained this answer,,,and then give a valid proof to a valid method for my previous thread i'd appreciate the help,,

    Q: Random variables x and y have jonint density function exp(-x-y) x.y>o

    findp(x>y) answer back of book is 1/2

    same as there

     \displaystyle \int _{0} ^{\infty} \;dy \int _{0} ^{y} e^{-x-y} \;dx

    after solving :

     \displaystyle  \int _{0} ^{y} e^{-x-y} \;dx = -\sinh{y} + \sinh{2y} +\cosh{y} -\cosh{2y}

    and then :

     \displaystyle \int _{0} ^{\infty} (\cosh{y}-\cosh{2y}-\sinh{y} + \sinh{2y})\;dy = \frac {1}{2}


    P.S. hope u know to work with hyperbolic functions


    just to note that

    \displaystyle \int e^{(-x-y)} dx =\int e^{(-x-y)} dy = -e^{(-x-y)} ==\sinh{(x+y)} - \cosh{(x+y)}
    Last edited by yeKciM; August 10th 2010 at 12:31 PM.
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  3. #3
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    yeh thanks everyone
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