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Math Help - Show whether they r independent!

  1. #1
    Senior Member
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    Show whether they r independent!

    Two independent random variables X,Y uniformly distrubited in [0,1]
    let U= X+Y V=X/Y
    Show whether U and V are independent
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  2. #2
    Senior Member tukeywilliams's Avatar
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     f_{X}(x) = f_{Y}(x) = \begin{cases} 1 \ \ \ 0 \leq x \leq 1 \\ 0 \ \ \ \text{otherwise} \end{cases}

     f_{U}(u) = \int_{- \infty}^{\infty} f_{X}(u-y)f_{Y}(y) \ dy

    Then  f_{U}(u) = \int_{0}^{1} f_{X}(u-y) \ dy

     f_{U}(u) = \begin{cases} u, \ \ \ \ \ \ \ \ \ 0 \leq u \leq 1 \\ 2-u, \ \ \ 1 < u \leq 2 \\ 0 \ \ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{cases}
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