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Math Help - uniform distribution problem

  1. #1
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    uniform distribution problem

    Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

    hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

    Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.
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  2. #2
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    Quote Originally Posted by Evan.Kimia View Post
    Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

    hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

    Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.
    P(Y\le y)=P(-2\ln (X)\le y)=P(X\ge e^{-y/2})= ...

    and

    f_Y(y)=\dfrac{\partial}{\partial y} P(Y\le y)

    CB
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  3. #3
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    Quote Originally Posted by Evan.Kimia View Post
    Let X have the uniform distribution U(0,1). Find the distribution function and then the p.d.f of Y = -2lnX

    hint: Find P(Y<=y) = P(X>=e^(-y/2) when 0 <y < infinity)

    Im having a hard time solving this problem, could anyone help me start it/give suggestions? Thanks.
    And when you think you have the answer, you can use the Probability Integral Transform Theorem to check it - the calculation takes 2 lines - (and if you're allowed to ignore the hint, you can go straight to the theorem).
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