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Math Help - Simple question need answer #2

  1. #1
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    Question Simple question need answer #2

    2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate
    a) P(X<0.5, Y<0.5)
    b) P(X<0.5)
    c) P(Y<0.5)

    Thanks~
    Last edited by mr fantastic; September 8th 2009 at 04:57 AM. Reason: Moved to new thread
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  2. #2
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    2a)

     <br />
\int_{0}^{a}\int_{0}^{x}2\cdot(x+y)\;dy\;dx\;=\;\f  rac{1}{2}<br />

    Solve for 'a'.
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  3. #3
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    what's the difference between 2a and 2b?

    what's the difference between 2a and 2b in this case?
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  4. #4
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    Quote Originally Posted by ugling View Post
    2. Given the density f(x,y)=2(x+y), 0<x<1, 0<y<x, calculate
    a) P(X<0.5, Y<0.5)
    b) P(X<0.5)
    c) P(Y<0.5)

    Thanks~
    a.  \int_{x = 0}^{x = 1/2}\int_{y = 0}^{y = x}2 \cdot (x+y)\; dy \; dx

    b. Same as above.

    c.  \int_{y = 0}^{y = 1/2}\int_{x = y}^{x = 1}2 \cdot (x+y)\; dx \; dy

    In each case it helps to draw the required region of integration to get the integral terminals.
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    2a)

     <br />
\int_{0}^{a}\int_{0}^{x}2\cdot(x+y)\;dy\;dx\;=\;\f  rac{1}{2}<br />

    Solve for 'a'.
    So, I'm just making up my own problems, today. Sorry about that.
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  6. #6
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    Quote Originally Posted by TKHunny View Post
    So, I'm just making up my own problems, today. Sorry about that.
    It's a good question though
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  7. #7
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by ugling View Post
    what's the difference between 2a and 2b in this case?
    shakespeare
    2b or not 2b
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