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Math Help - change of variable

  1. #1
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    change of variable

    X is a differentiable distribution funciton with pdf f_X
    g is continuously differentiable and one-one. let Y = g(x).

    f_Y (y) = f_X (h(y)) |det (\partial h / \partial y)|
    where \partial h / \partial y is the Jacobian matrix (\partial h_i / \partial y_i)_{1\leq i,j \leq k}

    can somebody explain this with a concrete example??
    and what is the meaning of multiplying a Jacobian determinant??

    thanks a lot
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  2. #2
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    Quote Originally Posted by graticcio View Post
    X is a differentiable distribution funciton with pdf f_X
    g is continuously differentiable and one-one. let Y = g(x).

    f_Y (y) = f_X (h(y)) |det (\partial h / \partial y)|
    where \partial h / \partial y is the Jacobian matrix (\partial h_i / \partial y_i)_{1\leq i,j \leq k}

    can somebody explain this with a concrete example??
    and what is the meaning of multiplying a Jacobian determinant??

    thanks a lot
    Read this thread: http://www.mathhelpforum.com/math-he...-function.html
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