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Joint CDF (proof)

  1. May 10, 2007 #1

    Zen

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  2. jcsd
  3. May 10, 2007 #2
    OK
    So here's how we did this:
    Let [tex]G_{x,y}=( \omega \in \Omega|X(\omega)\leq x,Y(\omega)\leq y)=(X\leq x,Y\leq y)[/tex]
    then
    [tex]P(G_{x,y})=P(X\leq x,Y\leq y)=F(x,y)[/tex]
    then
    [tex]P(a<X<b,c<Y<d)=G_{b,d}\setminus (G_{a,d}\cup G_{b,c})[/tex]
    then break up the RHS:
    [tex]P(G_{b,d})-[P(G_{a,d})+P(G_{b,c})-P(G_{a,d}\cap G_{b,c})][/tex]
    can you go from there?
     
    Last edited: May 10, 2007
  4. May 11, 2007 #3

    Zen

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    Thanks, I got it know. I also found the error in my original proof: P((B intersect D) U (A intersect C)) != 1
     
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