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How to calculate this probability (conditional distributions)

  1. Apr 24, 2013 #1
    fXY(x,y)=2 if 0<x<1 and x<y<1, 0 for other intervals
    I have to calculate: P((x>0.5)π(y<0.5)).
    I think it 0 but im not sure because in all other exercises ive made the surfaces intersect each other. Like in fig 1 for P((x<0.5))π(y<0.5))=integral from 0 to 0.5 from integral from x to 0.5 from 2dydx.
    The fig 2 is for P((x>0.5)π(y<0.5)).
    Im sorry because i forgot to mark the axis. vertical is y and horizontal is x.I apologize.
    https://www.physicsforums.com/attachment.php?attachmentid=58161&stc=1&d=1366802927
    https://www.physicsforums.com/attachment.php?attachmentid=58162&stc=1&d=1366802927
     

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    • fig2.png
      fig2.png
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  2. jcsd
  3. Apr 24, 2013 #2

    mathman

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    Gold Member

    If I understand your description, the density function = 0 for x > y. Therefore P((x > 0.5) and (y < 0.5)) = 0.
     
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