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Thread: 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:
    $\displaystyle f_{X}(x) = \frac{1}{b-a} = \frac{1}{1-0}$

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

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

    Then the pdf is the derivative of this
    $\displaystyle f_{Y}(y) =\begin{cases} 0 & y<0 \\ 2y & 0<y \leq 1 \\0 & y>1 \\ \end{cases}
    $
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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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