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Math Help - another bivariate stat question

  1. #1
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    another bivariate stat question

    f(x,y) = \left\{ \begin{array}{rcl}<br />
k(1-y) & \mbox{for} & 0 \leq x \leq y \leq 1 \\ <br />
0 & \mbox{for} & \mbox{other}<br />
\end{array}\right.

    for 0 \leq x \leq y \leq 1 is it 0 \leq x \leq 1 \ \mbox{and} \ x \leq y \leq 1 which would give:

    \int_{0}^{1} \int_{x}^{1} k(1-y) \ dy \ dx ?

    b) and does it matter if it's 0 \leq x \leq 1 \ \mbox{and} \ x \leq y \leq 1 or 0 \leq y \leq \ 1 \ \mbox{and} \ 0 \leq x \leq y ?

    c) and would P(x \leq \frac{3}{4}, \ y \geq \frac{1}{2}) be the same as 0 \leq x \leq \frac{3}{4}, \ \frac{3}{4} \leq y \leq 1?

    therefore: \int_{0}^{0.75} \int_{0.75}^{1} k(1-y) \ dy \ dx
    Last edited by lllll; April 6th 2008 at 09:35 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lllll View Post
    f(x,y) = \left\{ \begin{array}{rcl}<br />
k(1-y) & \mbox{for} & 0 \leq x \leq y \leq 1 \\ <br />
0 & \mbox{for} & \mbox{other}<br />
\end{array}\right.

    for 0 \leq x \leq y \leq 1 is it 0 \leq x \leq \ \mbox{and} \ x \leq y \leq 1 which would give:

    \int_{0}^{1} \int_{x}^{1} k(1-y) \ dy \ dx ?

    and does it matter if it's 0 \leq x \leq 1 \ \mbox{and} \ x \leq y \leq 1 or 0 \leq y \leq \ 1 \ \mbox{and} \ 0 \leq x \leq y ?
    no, you are correct. x goes from 0 up to y, but y goes up to 1, so x goes up to 1. y goes from x up to 1. so you get the integral you posted
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