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Math Help - Joint density

  1. #1
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    Joint density

    I have a joint density function

     f(x,y)= 3x, 0 \leq Y \leq X \leq 1

    And I have to find

     P(X \leq 1/2 , Y \leq 1/3)

    I integrated 0 to X dy and 0 to 1/3 dx

    Obviously I'm doing something wrong since that is not the answer in the book. So a little help would be appreciated.
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  2. #2
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    what did u get if u do directly
    with 0 to1/2 dx and 0 to 1/3 dy
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  3. #3
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    I tried to go directly buy I still get the wrong answer.
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  4. #4
    MHF Contributor matheagle's Avatar
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    try drawing the region....

    \int_0^{1/3}\int_y^{1/2}3xdxdy
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  5. #5
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    Quote Originally Posted by matheagle View Post
    try drawing the region....

    \int_0^{1/3}\int_y^{1/2}3xdxdy

    That gives me the right answer. I drew the region and that's where I made a mistake. Now it's all clear.

    Thanks
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