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Math Help - evaluate expected value (normal distribution)

  1. #1
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    evaluate expected value (normal distribution)

    I have to evaluate the expectation of the following function and no clue how to do it.

    E ( (x-k)^{-gamma}), where gamma is a positive integer larger than 1, k is a constant and x follows a normal distribution N(mu, simga^2).
    (1) Is it possible to find an expression for this expectation?
    (2) What is this expression (maybe with restrictions on gamma)? Is it obtained with the help of integration by parts?

    Thanks a lot!
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  2. #2
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    Quote Originally Posted by jazz123 View Post
    I have to evaluate the expectation of the following function and no clue how to do it.

    E ( (x-k)^{-gamma}), where gamma is a positive integer larger than 1, k is a constant and x follows a normal distribution N(mu, simga^2).
    (1) Is it possible to find an expression for this expectation?
    (2) What is this expression (maybe with restrictions on gamma)? Is it obtained with the help of integration by parts?

    Thanks a lot!
    Do you know how to at least set up the integral?
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  3. #3
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    I set it up like this:
    Int (x-k)^{-gamma} f(x) dx
    where the integral goes from - infinity to + infinity and f(x) is the pdf of the normal distribution. Is it this what you mean?
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  4. #4
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    Quote Originally Posted by jazz123 View Post
    I set it up like this:
    Int (x-k)^{-gamma} f(x) dx
    where the integral goes from - infinity to + infinity and f(x) is the pdf of the normal distribution. Is it this what you mean?
    Yes. So what have you tried?
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  5. #5
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    Well, this is where I am lost. I have don't know how to continue. Do you have an idea?
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