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Math Help - joint distribution question

  1. #1
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    joint distribution question

    find the joint distribution of
    f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\ <br />
0  \ \ \mbox{elsewhere}<br />
\end{array}\right.

    considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?
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  2. #2
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    Quote Originally Posted by lllll View Post
    find the joint distribution of
    f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\ <br />
0  \ \ \mbox{elsewhere}<br />
\end{array}\right.

    considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?
    I'll give a detailed reply later when I have a chance (unless someone beats me to it)
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  3. #3
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    Quote Originally Posted by lllll View Post
    find the joint distribution of
    f(x,y) = \left\{ \begin{array}{rcl} 4xy & \mbox{for} & 0 \leq x \leq 1, 0 \leq y \leq 1 \\ <br />
0  \ \ \mbox{elsewhere}<br />
\end{array}\right.

    considering the fact that it's continuous, you can't have a table with infinitively values, so do you just omit the table and approach it another way?
    I've had a closer look ...... are you trying to calculate \Pr(X < x_1, Y < y_1). If so:

    \Pr(X < x_1, Y < y_1) = \int_{0}^{x_1} \int_{0}^{y_1} 4xy \, dy \, dx.
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