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Math Help - joint Probability density

  1. #1
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    joint Probability density

    If the joint probability density of X and Y is given by f(x,y) =
    {2 for x > 0, y > 0, x + y < 1
    {0 else,
    then find P(X + Y > 2/3) and P(X > 2Y).

    I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated
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  2. #2
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    Quote Originally Posted by noles2188 View Post
    If the joint probability density of X and Y is given by f(x,y) =
    {2 for x > 0, y > 0, x + y < 1
    {0 else,
    then find P(X + Y > 2/3) and P(X > 2Y).

    I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated
    Did you draw the diagrams?

    P(X + Y > 2/3) can be found using simple geometry. I get 2\left(\frac{1}{2} - \frac{4}{18}\right) = \frac{5}{9}.

    P(X > 2Y) can be found using simple geometry. I get 2 \left( \frac{1}{2} \cdot 1 \cdot h \right)

    where h is the y-coordinate of the intersection point of y = x/2 and y = 1 - x.
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  3. #3
    MHF Contributor matheagle's Avatar
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    what do you mean by "F(x,y) = 1/2"?
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  4. #4
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    Quote Originally Posted by matheagle View Post
    what do you mean by "F(x,y) = 1/2"?
    That was a misprint on my part. F(x, y) = 1/2 when P(X<= 1/2, Y<= 1/2)
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