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Marginal distributions.

  1. Feb 9, 2008 #1
    I'm not sure I understnad what is a marginal distribution, but i need to show that if F1,F2 are one dimensional cummulative distribution functions then I(x,y)=F1(x)F2(y) has F1 and F2 as its marginal distributions.

    well if I(x,y)=P(X<=x,Y<=y) and if X and Y are independent, then it equals: P(X<=x)*P(Y<=y), then F1(x)=P(X<=x) F2(y)=P(Y<=y)
    or in general: F1(x)=P(X<=x, Y[tex]\in[/tex]A) F2(y)=P(X [tex]\in[/tex] B Y<=y) where A and B are intervals where the r.vs Y and X are defined.

    but it's really a guess.
  2. jcsd
  3. Feb 9, 2008 #2


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    What is the definition of a marginal distribution? How does that def. apply to F1(x)F2(y)?
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