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Math Help - Transformation of variable

  1. #1
    Junior Member
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    Transformation of variable


    May I ask if my approach is valid? In attempting this I arrive at:
    f_{X}(x) = \frac{1}{b-a} = \frac{1}{1-0}

    Then finding the cdf of Y=U^{1/2} I have:
    F_{y}(y) = P(Y \leq y) = P(U^{1/2} \leq y) = \int_{0}^{y^2} f_{X}(x)\ dx = y^2 for 0 \leq y \leq 1

    So my cdf is
     F_{Y}(y) =\begin{cases}0             &     y<0                  \\ y^2        &    0<y \leq 1\\1           &    y>1                     \\ \end{cases}<br />

    Then the pdf is the derivative of this
     f_{Y}(y) =\begin{cases} 0             &     y<0                  \\ 2y        &    0<y \leq 1           \\0           &    y>1                     \\ \end{cases}<br />
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  2. #2
    Senior Member
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    Re: Transformation of variable

    That's fine.
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  3. #3
    Junior Member
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    Re: Transformation of variable

    Thank you for taking the time to look over it!
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