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Math Help - need help! intergration

  1. #1
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    need help! intergration

    Y is a random variable that is exponentially distributed with parameter k=2.
    Find E[Y].

    Anyone know how to intergrate 2ye^(-2y) w.r.t. y from 0 to infinity? I have no idea on it.
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  2. #2
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    Quote Originally Posted by winganger View Post
    Y is a random variable that is exponentially distributed with parameter k=2.
    Find E[Y].

    Anyone know how to intergrate 2ye^(-2y) w.r.t. y from 0 to infinity? I have no idea on it.
    by parts u=y \mbox{ and }dv=e^{-2ydy}

    The final result should be

    2 \int ye^{-2y}dy=2[\frac{-y}{2}e^{-2y}-\frac{1}{4}e^{-2y}]

    Good luck
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    by parts u=y \mbox{ and }dv=e^{-2ydy}

    The final result should be

    2 \int ye^{-2y}dy=2[\frac{-y}{2}e^{-2y}-\frac{1}{4}e^{-2y}]

    Good luck
    Thank you.
    May I ask one more question, that is, what is the value when putting y=infinity into
    2ye^(-2y) ?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by winganger View Post
    Thank you.
    May I ask one more question, that is, what is the value when putting y=infinity into
    2ye^(-2y) ?
    it is zero...since \lim_{x \to 0}\frac{2x}{e^{2x}}=0 you can acheive this limt due to L'hopitals rule or simple comparison of rates of increase
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