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Math Help - Joint density function

  1. #1
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    Joint density function

    Hello friends!

    Its great to be a part of this forum, and I am glad to make my first post here.
    There is a question of the joint probability density function that I am unable to get even the idea how to solve.
    Kindly help.

    Question:
    If x and y are two random variables having joint density function:
    f(x,y)= 1/8(6-x-y) 0 < x < 2, 2 < y < 4
    0 otherwise

    Find:
    1) P(x<1 ∩ y<3)
    2) P(x+y<3)

    Thanks in advance friends.
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  2. #2
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    Quote Originally Posted by Sarmadi View Post
    Hello friends!

    Its great to be a part of this forum, and I am glad to make my first post here.
    There is a question of the joint probability density function that I am unable to get even the idea how to solve.
    Kindly help.

    Question:
    If x and y are two random variables having joint density function:
    f(x,y)= 1/8(6-x-y) 0 < x < 2, 2 < y < 4
    0 otherwise

    Find:
    1) P(x<1 ∩ y<3)
    2) P(x+y<3)

    Thanks in advance friends.
    Start by drawing the area defined by 0 < x < 2, 2 < y < 4 on a set of axes. Do it twice (once for each part). Now shade the part of the area corresponding to
    1) x< 1 and y < 3.
    2) x + y < 3.

    Now use what you have drawn to set up the integral limits on the double integral of f(x, y).
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  3. #3
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    How would I know what area corresponds to "x< 1 and y < 3" or "x + y < 3"?
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  4. #4
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    Think of it like this: start by graphing y = 3. The area under this line would correspond to y < 3, while the area above the line would correspond to y > 3
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