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Math Help - [SOLVED] integration with two variables

  1. #1
    Member i_zz_y_ill's Avatar
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    [SOLVED] integration with two variables

    Hi im just trying to prove to myself that I can solve this integration. It is infact the distribution function to the exponential distribution derived from the gamma distribution when \alpha=1

    F_{x}(x)=\int_0^x(\lambda).exp[-(\lambda)x]dx=1-exp[-(\lambda)x]

    Im not sure how this is done. Two variables are chi and x. Could somebody show me the working for this, perhaps explain how the chi variable is dealt here.
    Thanks.
    Last edited by i_zz_y_ill; August 17th 2009 at 06:18 AM.
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  2. #2
    Moo
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    Quote Originally Posted by i_zz_y_ill View Post

    F_{x}(x)=\int_0^x\chi e^{-\chi x}dx=1-e^{-\chi x}
    Is this what you meant ?

    In that case, use an integration by parts
    chi will be like a constant, that's all
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  3. #3
    Member i_zz_y_ill's Avatar
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    could you show me please i dont quite get this?
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  4. #4
    Member i_zz_y_ill's Avatar
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    If \lambda is just a constant, then it should be this:

    -(\lambda)^2(exp[-(\lambda)x]-1) which gives me the right answer when i take the minus inside the brackets but where does the \lambda^2go from here?
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  5. #5
    Member i_zz_y_ill's Avatar
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    ok If lambda is just a constant surely you can just take it out the brackets giving an answer of \lambda[-exp[-\lambda.x]+1] why is there a lambda still there?
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  6. #6
    Member i_zz_y_ill's Avatar
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    oh right yeah iman idiot gotitnow!
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  7. #7
    Moo
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    I hope it's okay, I wasn't connected and didn't understand much of your modifications
    (and it was a chi, not a lambda...but it doesn't matter)
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