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Math Help - E[x^(-1/2)] of exponential distribution

  1. #1
    MJM
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    E[x^(-1/2)] of exponential distribution

    have a hard time to calculate the expected value below
    E[x^(-1/2)], x is an exponential distribution of beta. I tried to transformed to a gamma but not succeed. the interal is way too big for me figure out. Thanks.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by MJM View Post
    have a hard time to calculate the expected value below
    E[x^(-1/2)], x is an exponential distribution of beta. I tried to transformed to a gamma but not succeed. the interal is way too big for me figure out. Thanks.
    You need to compute \int_0^\infty \frac{\beta e^{-\beta x}}{\sqrt{x}}dx. You should try to substitute u=\sqrt{x}; it will give you an integral involving the Gaussian density function. From there you can conclude.
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  3. #3
    MJM
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    Thanks. It works nicely.
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